Explanation: A battery works through electrochemical reactions occurring between its electrodes and electrolyte. These reactions involve the movement of electrons due to differences in chemical potential. Inside the cell, chemical substances undergo oxidation and reduction processes, releasing stored energy. This released energy does not remain in chemical form; instead, it drives electrons through an external circuit. The movement of these charged particles produces electric current, which can then power devices. The entire working principle is based on energy conversion, where stored internal energy becomes usable electrical output. This process is widely used in portable devices, vehicles, and backup systems. The concept is also tied to the law of conservation of energy, which states that energy only changes form and is not destroyed. Batteries are therefore practical examples of controlled energy transformation systems in everyday life.
Option b – Chemical energy to electrical energy
Identify the incorrect statement about energy.
A) Energy due to a body’s position or deformation is termed potential energy.
B) A Mass (m) moving at velocity (v) has kinetic energy equal to (mv/2).
C) The gravitational potential energy of a Mass (M) raised by a height (H) from Earth’s surface is MgH.
D) A moving object has what is known as kinetic energy.
Explanation: This question evaluates conceptual clarity about kinetic and potential energy along with their mathematical representations. Energy associated with motion depends on both Mass and velocity, and its standard form includes velocity squared, showing nonlinear dependence on speed. Potential energy is related to position or configuration in a field, such as gravitational or elastic systems. Gravitational potential energy depends on Mass, gravitational acceleration, and height from a reference level. A moving object indeed possesses kinetic energy due to its motion. However, incorrect formulations often arise when kinetic energy expressions are misrepresented or when proportional relationships are confused with exact equations. Understanding these distinctions is important in mechanics because energy calculations are used to analyze motion, work, and system behavior. The idea of energy conservation also connects both forms, where energy continuously transforms between kinetic and potential states in physical systems like falling bodies or oscillating objects.
Option b – A Mass (m) moving at velocity (v) has kinetic energy equal to (mv/2).
Hydroelectric power plants use falling water to spin turbines. The rotation of the shaft converts the water’s potential energy into ______ energy.
A) Chemical
B) Thermal
C) Gravitational
D) Kinetic
Explanation: Hydroelectric power systems rely on stored energy in water held at a height. This stored energy is due to gravity acting on the Mass of water, giving it the ability to do work when released. As water flows downward, its stored energy begins transforming into motion-based energy because the water gains speed while descending. This moving water strikes turbine blades, causing mechanical rotation of the shaft connected to a generator. The key idea is the conversion of stored positional energy into energy associated with motion. This transformation is a classic example of energy conservation in action, where energy changes form but total energy remains constant throughout the process. The rotating turbine is the intermediate stage that converts Fluidmotion into mechanical rotation, which is later converted into electrical output in power stations.
Option d – Kinetic
James Prescott Joule established the foundation of the principle of conservation of ______.
A) Gravitational phenomena
B) Theory of vibrating receptacles
C) Gas diffusion concepts
D) Kinetic and potential energies forming mechanical energy
Explanation: This question relates to a fundamental principle in Physics describing how energy behaves in isolated systems. Joule’s experiments demonstrated that different forms of energy are interconvertible, especially linking mechanical work with thermal effects. His findings helped establish that energy is not lost but changes form during physical processes. For example, when mechanical work is done, it can produce Heat, and vice versa. This understanding led to the broader principle that all energy transformations obey a conservation rule. The concept plays a crucial role in mechanics, Thermodynamics, and electrical systems. It helps explain how systems maintain a constant total energy even when energy shifts between kinetic, potential, thermal, and other forms. Joule’s contribution was key in formalizing this unified view of energy behavior in nature.
Option a – Gravitational phenomena
Kinetic and potential energies together make up ______ energy.
Explanation: In mechanics, energy associated with motion is classified as kinetic energy, while energy stored due to position or configuration is called potential energy. In many physical systems, especially those involving motion under forces like gravity or elasticity, both forms of energy coexist and transform into each other continuously. The combined total of these two forms represents the overall energy possessed by a system due to motion and position effects together. This combined form is particularly important in systems where objects move under conservative forces, such as falling objects, pendulums, and springs. The total remains constant if no external non-conservative forces act. This concept forms the basis for solving many problems involving motion, energy transfer, and system dynamics in classical mechanics.
Option c – Mechanical
Which example illustrates gravitational potential energy?
A) Moving car
B) Bullet shot from a gun
C) Water stored behind a dam
D) Foot kicking a ball
Explanation: Gravitational potential energy refers to the energy stored in an object due to its position in a gravitational field, especially when it is located at a height above a reference level. This energy depends on the object’s Mass, the gravitational field strength, and its vertical position. Objects placed at higher elevations have greater stored energy because gravity can do more work on them when they fall. In practical situations, reservoirs, raised objects, or elevated masses are typical examples of systems storing this type of energy. When such objects are released, their stored energy transforms into motion-based energy. This principle is widely used in engineering systems like dams and elevated storage structures where controlled release of energy is essential for power generation and mechanical work.
Option c – Water stored behind a dam
The standard commercial unit used to measure electric energy is ______.
A) Watt-hour
B) Watt per hour
C) Kilowatt hour
D) Kilowatt per hour
Explanation: Electrical energy consumption in practical life is measured using a standardized commercial unit that reflects the amount of electrical work done over time. This unit is widely used by Electricity providers to calculate household and industrial energy usage. It represents energy consumed when a certain amount of power is used continuously for a specific duration. The concept links power, time, and energy into a single measurable quantity. Larger units are preferred for billing purposes because everyday electrical usage involves significant energy over long periods. This unit is derived from the relationship between power (rate of energy consumption) and time, making it suitable for real-world applications such as billing Electricity usage in homes, industries, and commercial establishments.
Explanation: In atomic and subatomic Physics, energy values are often extremely small compared to everyday mechanical energy scales. To measure such tiny energy changes conveniently, a specialized unit is used based on the energy gained by an electron when it moves through a potential difference of one volt. This unit is particularly useful in studying Atomic Structure, particle Physics, and electronic transitions. It allows scientists to express energy levels of electrons in atoms and other microscopic systems in a simplified numerical form. The concept is closely linked to electric potential difference and charge interaction at the microscopic level. It is widely used in fields like semiconductor Physics, quantum mechanics, and nuclear science for representing energy at very small scales.
Option b – Energy
Approximately how many joules of mechanical energy equal one calorie of Heat energy?
A) 0.24
B) 0.48
C) 4.2
D) 2.4
Explanation: This question deals with the relationship between different energy units used in mechanics and Thermodynamics. Mechanical energy is commonly measured in joules, while Heat energy is often expressed in calories. A calorie is defined based on the amount of Heat required to raise the temperature of a small quantity of water by a specific amount under standard conditions. Experiments in Thermodynamics show a fixed conversion relationship between these two units, meaning energy expressed in one system can be converted into the other using a constant factor. This equivalence is important in understanding the mechanical equivalent of Heat, which established that Heat and mechanical work are interchangeable forms of energy. This principle is widely used in Physics, Chemistry, and engineering while solving problems involving Heat transfer and energy conversion.
Option c – 4.2
Pascal is the SI unit of ______, representing a force of 1 N applied evenly over 1 m².
Explanation: This question focuses on the concept of pressure in Physics. Pressure is defined as the force applied per unit area on a surface. When a force acts on a surface and is distributed over a specific area, it produces a measurable effect depending on how concentrated the force is. A smaller area results in higher pressure for the same force, while a larger area reduces it. The SI unit of pressure is derived from the fundamental units of force and area, combining them into a standard measurement used in science and engineering. This concept is widely applied in Fluid mechanics, atmospheric studies, hydraulics, and everyday phenomena such as tire inflation and Fluid flow systems. Understanding pressure helps in analyzing how forces interact with surfaces in both Solid and Fluid systems.
Option a – Pressure
A cricket ball weighing 160 g is dropped from 50 m. What is its kinetic energy just before hitting the ground? (g = 10 m/s²)
A) 50 joules
B) 80 joules
C) 160 joules
D) 8 joules
Explanation: This question is based on the conservation of mechanical energy in a gravitational field. When an object is dropped from a height, it initially possesses gravitational potential energy due to its position. As it falls, this stored energy is gradually converted into kinetic energy as the object gains speed. Neglecting air resistance, the total mechanical energy remains constant throughout the motion. Just before hitting the ground, nearly all the initial potential energy has transformed into kinetic energy. The calculation involves Mass, gravitational acceleration, and height, showing how energy depends on physical parameters. This principle is widely used in analyzing free fall motion and energy transformations in mechanical systems.
Option b – 80 joules
Before it is released, a yo-yo primarily possesses ______ energy.
Explanation: This question is based on the idea of stored energy due to position or configuration. A yo-yo held at a height above the ground has energy because of its position in Earth’s gravitational field. This energy is stored and can be released when the object is allowed to move downward. Before release, there is no significant motion, so the energy is not associated with movement but with position. When released, this stored energy begins converting into motion-based energy as the yo-yo falls and unwinds. This transformation illustrates the continuous interchange between stored and kinetic forms of energy in mechanical systems. The concept is widely used to explain motion under gravity and energy conservation in simple mechanical devices.
Explanation: This question tests the understanding of physical quantities and their measurement units. Energy is a scalar physical quantity that represents the capacity to do work and is measured in standard units such as joule and related practical units like calorie and kilowatt-hour. Not all physical quantities represent energy, even if they appear in scientific contexts. Some quantities like force or momentum have different dimensional formulas and cannot be classified as energy. Correct identification requires understanding dimensional analysis and the distinction between energy and non-energy quantities. Energy units are derived from fundamental mechanical relationships involving force and displacement. Recognizing valid energy units is important in Physics for correct application in calculations involving work, power, and thermodynamic processes.
Option d – Joule, Calorie, Kilowatt hour
Who formulated the laws of levers and pulleys, enabling heavy objects to be moved with minimal force?
A) Archimedes
B) Eudoxus
C) Pythagoras
D) Democritus
Explanation: This question is about the historical development of mechanics and simple machines. The study of levers and pulleys focuses on how forces can be multiplied or redirected to make work easier. A lever operates on the principle of moments, where a small force applied at a longer distance from a pivot can balance or move a larger force at a shorter distance. Pulleys similarly help in lifting heavy loads by changing the direction of force and distributing weight across multiple segments of a rope. These principles are fundamental in classical mechanics and form the basis of many engineering tools and devices. The understanding of such systems helped establish early mechanics as a scientific discipline, influencing later developments in Physics and engineering applications involving force, motion, and equilibrium.
Option a – Archimedes
Which pair of quantities shares identical dimensions?
A) Power and radius of circular motion
B) Work and angular displacement
C) Work and torque
D) Power and moment of inertia
Explanation: This question tests the concept of dimensional analysis, which is used to compare physical quantities based on their fundamental units like Mass, length, and time. Two quantities are said to have identical dimensions if they can be expressed using the same combination of these fundamental units. This method is useful for verifying physical equations and understanding relationships between different physical concepts. Quantities like work, energy, and torque often share similar dimensional forms because they involve force acting over distance. However, physical interpretation still differs even if dimensions are similar. Dimensional analysis helps in identifying errors in equations and ensuring consistency in physical formulas across mechanics and related fields.
Option c – Work and torque
Which of these is not an energy unit?
A) Joule
B) Calorie
C) Kilowatt hour
D) Newton
Explanation: This question focuses on distinguishing energy units from other physical quantities. Energy is measured in units that represent the ability to do work, such as joules, calories, and kilowatt-hours. These units are derived from mechanical or thermal energy concepts. However, not all scientific units represent energy; some measure entirely different physical properties like force, pressure, or mass. Force-related units are not energy units because they describe interaction rather than capacity to perform work. Understanding this distinction is important in Physics because confusing units can lead to incorrect interpretation of physical equations and results. Proper classification of units ensures correct application in calculations involving work, energy conversion, and physical system analysis.
Option d – Newton
In a metro station, about 20 people per minute ascend an escalator to a height of 15 m. If each person averages 50 kg and g = 10 m/s², what is the escalator’s power output?
A) 1.25 kW
B) 2.5 kW
C) 150 kW
D) 15 kW
Explanation: This question is based on the concept of power, which is the rate at which work is done or energy is transferred. When people are lifted upward, work is done against gravity. The energy required depends on mass, gravitational acceleration, and height gained. Since multiple people are involved per unit time, the total energy transferred per minute becomes important. Power is calculated by dividing total work done by time taken. In this situation, the escalator continuously performs mechanical work by raising people against gravitational force. This makes it a practical example of energy conversion in real-life systems where mechanical energy is supplied to overcome gravitational potential energy. Understanding this helps in analyzing machines that operate continuously under load.
Option b – 2.5 kW
At 1 bar pressure, a fixed amount of hydrogen gas occupies 2.27 litres. What will be its volume if pressure drops to 0.2 bar?
A) 12,250 cm³
B) 11,350 cm³
C) 10,270 cm³
D) 11.35 cm³
Explanation: This question is based on the relationship between pressure and volume in gases. When temperature remains constant, gases follow an inverse relationship between pressure and volume. This means that when pressure decreases, volume increases proportionally, and vice versa. This behavior is a key concept in gas laws and is widely used in understanding gas behavior in closed systems. Hydrogen gas, like other gases, expands when external pressure is reduced because the particles have more space to move. This principle is important in Chemistry and Physics for predicting how gases behave under different environmental conditions, such as in cylinders, balloons, and atmospheric systems. The inverse relationship allows calculations involving changes in physical conditions without altering the amount of gas present.
Option b – 11,350 cm³
Two objects, A (2 kg) and B (3 kg), fall from different heights. A takes 5 seconds and B 3 seconds to reach the ground. What is the ratio of their kinetic energies on impact?
A) 10/9
B) 2/3
C) 5/3
D) 50/27
Explanation: This question is based on energy gained during free fall under gravity. When an object falls freely, its gravitational potential energy gradually converts into kinetic energy as it accelerates downward due to gravity. The final kinetic energy just before impact depends on the speed acquired during the fall, which in turn depends on the time of fall when acceleration is constant. Since heavier objects store more potential energy and longer fall time leads to greater velocity, both mass and motion duration influence the final energy. In ideal free fall (neglecting air resistance), the motion is uniformly accelerated, so velocity increases linearly with time and kinetic energy depends on the square of velocity. Therefore, comparing two falling bodies involves relating mass and time-based velocity growth to determine how their final energy states compare at impact.
Option d – 50/27
Which of these is not a recognized unit of pressure?
A) Pascal (Pa)
B) N/m²
C) J/m²
D) Bar
Explanation: This question deals with identifying correct physical units of pressure. Pressure is defined as force acting per unit area, so its unit is derived from force divided by area. Standard units like pascal and bar are widely accepted in physics and engineering. These units are used in Fluid mechanics, atmospheric science, and material studies. However, some units may resemble energy or other physical quantities rather than pressure, leading to confusion. Energy-related units are not valid for pressure because they represent work or energy transfer rather than force distribution over an area. Understanding unit classification is important to avoid mistakes in calculations involving gases, fluids, and mechanical systems where pressure plays a key role in system behavior.
Option c – J/m²
If a moving object’s linear momentum doubles, its kinetic energy changes by a factor of ______.
A) 2
B) 4
C) 6
D) 8
Explanation: This question explores the relationship between momentum and kinetic energy in classical mechanics. Linear momentum depends on both mass and velocity, while kinetic energy depends on the square of velocity. When momentum changes, it implies a change in velocity (assuming mass remains constant). Since kinetic energy is proportional to the square of velocity, any change in momentum produces a non-linear change in energy. This means energy does not increase in the same proportion as momentum but follows a squared relationship. Understanding this connection helps in analyzing motion, collisions, and energy transfer between interacting bodies. It is especially important in systems where objects undergo sudden changes in motion, such as impacts or explosions, where both momentum conservation and energy transformation principles are applied.
Option b – 4
Which statement is correct for a freely falling object?
A) It moves with a uniform velocity.
B) It moves with a uniform speed.
C) It moves with a non-uniform acceleration.
D) It moves with a uniform acceleration.
Explanation: This question is based on motion under gravity. A freely falling object moves under the influence of gravitational force alone, assuming air resistance is negligible. In such motion, acceleration remains constant because gravitational acceleration near Earth’s surface does not change significantly with height over small distances. However, velocity continuously changes because the object keeps gaining speed as it falls. This means the motion is not uniform in speed, but it is uniform in acceleration. Understanding this distinction is essential in kinematics, as it helps differentiate between constant velocity motion and constant acceleration motion. This concept is widely used in solving equations of motion and analyzing vertical motion problems in physics.
Option d – It moves with a uniform acceleration.
A cannon fires a ball upward at 100 m/s. The total flight time is 20 s before it lands. After hitting the ground, it retains only 30% of its speed. To what height will it rise after the first bounce? (g = 10 m/s²)
A) 70 m
B) 100 m
C) 45 m
D) 50 m
Explanation: This question involves energy loss during motion and rebound. When an object is projected upward, it initially has kinetic energy which gets converted into gravitational potential energy as it rises. At the highest point, velocity becomes zero, and energy is fully stored as potential energy. During descent and impact with the ground, some energy is lost due to deformation, sound, and Heat, so the object does not retain full kinetic energy after bouncing. After impact, only a fraction of its original speed remains, which reduces the available kinetic energy significantly. The height reached after bouncing depends on this reduced energy because height is directly related to the square of velocity. This illustrates real-world energy dissipation in inelastic collisions.
Option c – 45 m
An iron nail sinks in water, but an iron ship remains afloat. Which of the following statements correctly explains this observation? a) The ship’s average density is greater than that of water b) The iron nail’s average density is greater than that of water c) The ship’s average density is lower than that of water d) The ship’s average density is equal to that of water. Select the correct code:
a) 2 and 3
b) 1 and 2
c) 1 and 4
d) 2 and 4
Explanation: This question is based on buoyancy and density concepts in Fluid mechanics. When an object is placed in a Fluid, it experiences an upward force called buoyant force. Whether an object sinks or floats depends on its average density compared to the Fluid. A Solid iron nail has a high density and displaces a small volume of water, so it cannot generate enough upward force to balance its weight. However, a ship, although made of iron, is hollow and contains air, which reduces its average density significantly. Because of its large volume, it displaces enough water to produce sufficient buoyant force to stay afloat. This demonstrates Archimedes’ principle, which explains floating and sinking behavior in fluids based on density and displaced Fluid weight.
Option a – 2 and 3
Earth’s escape velocity is about 11.2 km/s. On a planet with half the Earth’s radius and four times its mass density, the approximate escape speed (in km/s) would be:
a) 11.2
b) 15.8
c) 7.9
d) 5.6
Explanation: This question is based on gravitational escape velocity, which is the minimum speed needed for an object to leave a planet’s gravitational field without returning. Escape velocity depends on the planet’s mass and radius, where stronger gravity requires higher speed to overcome it. If a planet has different physical properties such as radius and density, its mass changes accordingly because mass depends on volume and density. Since volume scales with the cube of radius, any change in radius significantly affects mass and therefore gravitational strength. Escape velocity increases with greater gravitational pull and decreases with larger radius if mass remains constant. This relationship helps compare planetary gravitational fields and understand how celestial bodies retain or lose atmospheric gases.
Option b – 15.8
Two planets have masses in the ratio 1 : 7, and their diameters are in the ratio 2 : 1. The ratio of the gravitational forces they exert on each other is:
a) 1 : 7
b) 7 : 1
c) 2 : 1
d) 1 : 1
Explanation: This question is based on Newton’s law of Gravitation, which describes the force between two masses. Gravitational force depends directly on the product of the two masses and inversely on the square of the distance between their centers. When comparing two planets, both their masses and separation distance must be considered. Diameter determines the distance between centers when they are in contact or at a given separation. Since force depends on inverse square of distance, even small changes in size significantly affect the interaction. Understanding this relationship helps in comparing gravitational interactions between celestial bodies and analyzing how mass distribution and spacing influence gravitational strength in space systems.
Option d – 1 : 1
The gravitational pull exerted by Earth on a body is known as:
a) Mass of the body
b) Weight of the body
c) Density of the body
d) Magnitude of the body
Explanation: This question focuses on the concept of force due to gravity acting on objects near Earth. Every object with mass experiences an attractive force toward Earth’s center. This force depends on the object’s mass and gravitational field strength. It is commonly experienced as the weight of an object, which is the force acting on it due to gravity. Weight varies depending on location because gravitational strength changes with altitude, depth, and planetary body. Unlike mass, which remains constant, this force depends on external gravitational conditions. Understanding this concept is essential in mechanics because it distinguishes between intrinsic property (mass) and force experienced due to gravitational interaction. It is widely used in engineering, physics, and space science calculations.
Option b – Weight of the body
Identify the statement that is incorrect:
a) Every object in the universe attracts every other object due to gravity
c) The acceleration due to gravity (g) is zero at Earth’s center
d) Mass and weight are expressed in different units
Explanation: This question examines fundamental concepts of universal Gravitation and gravitational behavior. Gravity is a universal attractive force acting between all objects with mass. It governs planetary motion, tides, and object fall on Earth. However, gravitational acceleration is not uniform throughout Earth; it varies with position and becomes zero at the exact center due to symmetry. Mass and weight are different physical quantities with different units, where mass remains constant and weight depends on gravitational field strength. Understanding these distinctions is essential in mechanics, especially when analyzing motion under gravity and applying Newton’s law of Gravitation. Incorrect statements usually arise from confusion between mass, weight, and variation of gravitational effects in different locations.
Find the minimum power needed to raise a 50 kg mass through a height of 8 m in 10 s. (Take g = 10 m/s²)
a) 400 W
b) 40 W
c) 500 W
d) 50 W
Explanation: This question deals with power, which is the rate of doing work or transferring energy. When an object is lifted against gravity, work is done equal to the increase in its gravitational potential energy. This depends on mass, gravitational acceleration, and height. Power is then calculated by dividing this work by time taken. A shorter time requires higher power because the same amount of work is done more quickly. This concept is important in machines, elevators, and lifting systems where efficiency and speed Matter. It helps in understanding how energy usage changes with time and why high-power devices are needed for rapid mechanical work.
Option a – 400 W
Which scientific principle, formulated in the 17th century, states that pressure applied to a confined Fluid is transmitted equally in all directions, regardless of the container’s shape?
a) Magnus’s Law
b) Graham’s Law
c) Pascal’s Law
d) Torricelli’s Law
Explanation: This question is based on fluid mechanics and pressure transmission in enclosed systems. When pressure is applied to a confined fluid, it is transmitted uniformly throughout the fluid in all directions without loss. This principle explains how hydraulic systems work, where a small force applied at one point can produce a larger force at another point. It is widely used in hydraulic brakes, lifts, and presses. The key idea is that fluids transmit pressure equally because their particles move freely and distribute force evenly. This property allows mechanical advantage in engineering systems, making it easier to lift heavy loads using small input forces.
Option c – Pascal’s Law
Find the INCORRECT statement about the universal law of Gravitation.
a) It is the force that keeps us attached to Earth.
b) It is the force responsible for tides caused by the stars and Earth.
c) It is the force that governs the motion of planets around the Sun.
d) It is the force that keeps the Moon moving around the Earth.
Explanation: This question is about Newton’s universal law of Gravitation, which describes the attractive force between any two masses in the universe. This force is responsible for planetary motion, tides, and objects falling toward Earth. It acts between all Matter regardless of size or distance, although its strength depends on mass and separation. Gravitational effects are observed in systems ranging from small objects to large celestial bodies. Misconceptions often arise regarding its role in different natural phenomena or how it applies universally. Understanding this law helps explain orbital motion, weight, and large-scale cosmic interactions governed by mass attraction and distance relationships.
Option b – It is the force responsible for tides caused by the stars and Earth.
Select the correct fact about gravity.
a) The unit of g matches that of acceleration.
b) The unit of g matches that of velocity.
c) The unit of g matches that of mass.
d) The unit of g matches that of friction.
Explanation: This question is based on the nature of gravitational acceleration near Earth’s surface. Gravity produces a constant acceleration on freely falling objects, assuming air resistance is ignored. This acceleration has a fixed value at a given location and is independent of the mass of the falling object. It represents how quickly the velocity of a falling body changes over time due to Earth’s gravitational pull. The unit of this quantity is derived from distance and time squared, which classifies it under acceleration. It plays a central role in kinematics and equations of motion, especially in vertical motion problems. Understanding its unit and behavior helps distinguish it from quantities like velocity or mass, which describe different physical aspects of motion and Matter.
Option a – The unit of g matches that of acceleration.
The law expressed as T² ∝ R³, linking a planet’s orbital period to its orbital radius, is known as:
a) Hubble’s Law
b) Copernicus’s Law
c) Kepler’s Third Law
d) Bragg’s Law
Explanation: This question relates to planetary motion and the relationship between orbital time period and orbital radius. Planets moving around a central body follow predictable patterns where the time taken for one complete revolution depends on their distance from the central object. The square of the orbital period is proportional to the cube of the orbital radius, showing that planets farther away take significantly longer to complete an orbit. This relationship is fundamental in celestial mechanics and helps describe the structure of planetary systems. It also provides insight into gravitational influence on orbital motion and is used to compare different planetary orbits. This principle is widely applied in astronomy to determine distances and orbital characteristics of celestial bodies.
Option c – Kepler’s Third Law
Who formulated the three laws describing planetary motion?
a) Isaac Newton
b) Tycho Brahe
c) Johannes Kepler
d) Galileo Galilei
Explanation: This question refers to the development of classical astronomy and the laws governing planetary motion. These laws describe how planets move in elliptical orbits, how their speed varies depending on their position in orbit, and how their orbital period relates to their distance from the Sun. The formulation of these laws marked a major advancement in understanding celestial motion by replacing earlier circular orbit assumptions with more accurate elliptical models. These principles became the foundation for later gravitational theory and helped establish the connection between motion and force in space. They are essential in predicting planetary positions and understanding the dynamics of Solar system bodies.
Option c – Johannes Kepler
Who demonstrated that in a vacuum all objects fall with the same acceleration and reach the ground simultaneously?
a) Galileo Galilei
b) Thomas Alva Edison
c) Isaac Newton
d) Albert Einstein
Explanation: This question is based on experimental observations of free fall motion. When objects fall in the absence of air resistance, they experience only gravitational force, causing them to accelerate uniformly regardless of their mass. This means all objects, whether heavy or Light, fall at the same rate under ideal conditions. This concept challenged earlier beliefs that heavier objects fall faster. The demonstration of this idea involved controlled experiments showing identical acceleration for different objects in vacuum conditions. It laid the foundation for classical mechanics and helped establish the concept of uniform gravitational acceleration. This principle is widely used in physics to analyze motion and is fundamental to understanding gravity-driven systems.
Option a – Galileo Galilei
A 2 kg mass is dropped from a height of 10 m. What is the ratio of its potential energy to kinetic energy when it is at 5 m? (g = 10 m/s²)
a) 1 : 2
b) 1 : 1
c) 4 : 1
d) 1 : 4
Explanation: This question is based on energy conservation during free fall. When an object is dropped, its initial energy is entirely gravitational potential energy. As it falls, this energy gradually converts into kinetic energy due to increasing speed. At any intermediate height, the total mechanical energy remains constant if air resistance is ignored. The distribution between potential and kinetic energy depends on how much height has been lost. At halfway point in height, energy is shared between stored and motion-based forms in a predictable ratio. This concept is widely used in solving motion problems involving falling bodies, helping to understand how energy continuously transforms during gravitational acceleration.
Option b – 1 : 1
If G is the gravitational constant, M is Earth’s mass, and R is Earth’s radius, the correct formula for the acceleration due to gravity at the surface is:
a) GM / R²
b) GMR²
c) GM / R
d) GM² / R
Explanation: This question focuses on the relationship between gravitational force and acceleration due to gravity. The force experienced by an object near Earth depends on Earth’s mass and the distance from its center. Acceleration due to gravity is derived by applying Newton’s law of gravitation and dividing by the object’s mass, showing that it depends only on planetary properties and not on the falling object. The radius of Earth plays a key role because gravitational strength decreases with distance from the center. This relationship is fundamental in understanding weight, free fall, and motion under gravity. It is widely used in physics calculations involving planetary motion, satellite motion, and surface gravity comparisons.
Option a – GM / R²
Two identical iron spheres each of radius 1 m and density 3/(2π) kg/m³ are in contact. What is the gravitational force between them? (G = 6.67 × 10⁻¹¹ N·m²/kg²)
a) 0.667 N
b) 0.0667 N
c) 6.67 N
d) 66.7 N
Explanation: This question applies Newton’s law of gravitation to real objects. Gravitational force depends on the masses of the objects and the distance between their centers. To find mass, density and volume are used, where volume of a sphere depends on its radius cubed. Since the spheres are in contact, the distance between their centers equals the sum of their radii. Even though gravitational force is extremely weak between small objects, it can still be calculated using universal gravitation principles. This concept shows how even everyday objects attract each other, although the effect is usually negligible compared to Earth’s gravitational pull. It is important in understanding mass distribution and gravitational interaction at different scales.
Option c – 6.67 N
Which scientist’s principle states that the total energy per unit mass of a fluid in motion—comprising kinetic, potential, and pressure energies—remains constant?
a) Daniel Bernoulli
b) Evangelista Torricelli
c) Blaise Pascal
d) Marie Poiseuille
Explanation: This question is based on fluid dynamics and energy conservation in moving fluids. In a flowing fluid, energy exists in different forms such as kinetic energy due to motion, potential energy due to height, and pressure energy due to fluid pressure. The principle states that the sum of these energies per unit mass remains constant along a streamline in ideal conditions. This concept explains how fluid speed and pressure change in pipes, nozzles, and air flow systems. When fluid speed increases, pressure decreases, and vice versa. This principle is widely applied in aerodynamics, hydraulics, and engineering systems involving fluid motion and energy balance.
Option a – Daniel Bernoulli
Who introduced the term “horsepower” to describe engine output?
a) Amedeo Avogadro
b) John Dalton
c) James Watt
d) Albert Einstein
Explanation: This question relates to the historical development of power measurement in mechanical systems. Power represents the rate at which work is done or energy is transferred. To compare engine performance with practical work done by horses, a standard unit was introduced based on the average power output of a horse. This helped in quantifying engine efficiency during the early industrial period. The concept became widely adopted in engineering to describe mechanical output of engines and machines. It provides a practical way to compare energy conversion rates in real-world systems. This unit is still used today in automotive and mechanical contexts to describe engine performance and capacity.
Option c – James Watt
Which metric unit of pressure equals 0.986923 atm?
a) Quart
b) Yard
c) Bar
d) Gallon
Explanation: This question is based on pressure conversion between different measurement systems. Atmospheric pressure at sea level is commonly used as a reference standard in physics and Chemistry. Other pressure units are defined relative to this standard based on their numerical equivalence. The metric unit of pressure used in engineering and meteorology has a defined relationship with atmospheric pressure. Understanding these conversions is important for solving problems involving gas laws, fluid pressure, and environmental conditions. It helps in comparing measurements taken under different unit systems and ensures consistency in scientific calculations involving pressure-related phenomena.
Option c – Bar
For a book of mass m sliding a distance d on a smooth horizontal surface, the work done by gravity is:
a) Mgd
b) Md
c) md cos θ
d) 0
Explanation: Work done in physics depends on the component of force acting along the direction of displacement. Gravity acts vertically downward, while the book’s motion is purely horizontal on a smooth surface. Since the displacement has no vertical component, the angle between gravitational force and displacement is 90 degrees. When a force acts perpendicular to displacement, no energy transfer occurs in the direction of motion. The normal force balances the weight of the object, preventing vertical movement. Therefore, gravity does not contribute to the work done during horizontal motion in an ideal smooth surface scenario. This idea is important in understanding how different forces contribute to work depending on direction and motion constraints in mechanical systems.
Option d – 0
Which relation between atmospheric pressure and bar is accurate?
a) 1 atm = 1 bar
b) 1 atm = 1.013 bar
c) 1 atm = 1.013 × 10⁵ bar
d) 1 atm = 10⁵ bar
Explanation: This question focuses on standard pressure units and their conversion. Atmospheric pressure is a commonly used reference in physics, defined based on average air pressure at sea level. The bar is another unit used in meteorology and engineering, closely related to atmospheric pressure but defined using a rounded approximation for convenience. These units help simplify calculations involving gases, fluids, and environmental systems. Converting between them requires understanding their relative magnitudes and standard reference conditions. Such conversions are widely used in gas laws, weather measurements, and industrial applications where pressure values must be expressed consistently across different unit systems. Accurate knowledge of these relationships is essential for interpreting scientific data correctly.
Option b – 1 atm = 1.013 bar
Post-tensioning is most effective for:
a) Long spans
b) End spans
c) Edge spans
d) Break spans
Explanation: This question is based on structural engineering principles related to reinforced concrete systems. Post-tensioning is a technique where steel tendons are tensioned after concrete has been cast and hardened. This creates compressive stress within the structure, improving its ability to withstand tensile forces during loading. It is especially useful in structures that span long distances because it reduces cracking and increases load-bearing capacity. By introducing internal compression, the structure becomes stronger and more durable under bending stresses. This method is widely used in bridges, large slabs, and long-span constructions where traditional reinforcement may not be sufficient. It enhances structural efficiency and reduces material usage while maintaining strength and stability.
Option a – Long spans
When an object is thrown upward, at the highest point of its path:
a) Potential energy is greatest.
b) Both kinetic and potential energies are greatest.
c) Kinetic energy is greatest.
d) Both kinetic and potential energies are zero.
Explanation: This question is based on vertical motion under gravity and energy transformation. When an object is thrown upward, it initially possesses kinetic energy due to its velocity. As it rises, this kinetic energy gradually converts into gravitational potential energy because its height increases. At the highest point of motion, the velocity becomes momentarily zero before the object starts descending. At this instant, the energy is entirely stored in the form of potential energy relative to the reference level. This point represents a key concept in energy conservation, where motion-based energy is fully transformed into position-based energy. This principle is widely used in projectile motion analysis and helps in understanding how energy changes during upward and downward motion.
Option a – Potential energy is greatest.
Dividing thrust in a liquid by which quantity gives the pressure?
a) Volume
b) Area
c) Density
d) Mass
Explanation: This question is based on the definition of pressure in fluids. Pressure is defined as the force exerted per unit area on a surface. In fluid mechanics, thrust refers to the total force exerted by a fluid on a surface due to its weight and motion. To determine pressure, this total force must be distributed over the area on which it acts. This helps in understanding how fluids exert force on submerged objects and container walls. Pressure increases when the same force acts over a smaller area, which is why sharp objects exert higher pressure. This concept is fundamental in hydrostatics and is widely applied in engineering systems involving fluids and hydraulic devices.
Option b – Area
Which type of energy is displayed by falling coconuts, speeding vehicles, rolling stones, and flying aircraft?
a) Potential energy
b) Kinetic energy
c) Elastic energy
d) Radiant energy
Explanation: This question deals with energy associated with motion. Any object that is moving possesses energy due to its velocity. This form of energy depends on both mass and speed, meaning heavier and faster objects carry more of it. It is a fundamental form of mechanical energy observed in everyday life whenever objects are in motion. Examples include natural falling objects and engineered systems like vehicles and aircraft. This energy plays a major role in motion analysis, collisions, and energy transfer between interacting bodies. It continuously transforms into other forms of energy when motion changes due to external forces such as friction or gravity. Understanding this concept is essential in mechanics and real-world physics applications.
Option b – Kinetic energy
What is the average kinetic energy per Molecule of an ideal gas at 25 °C (in joules)?
a) 6.17 × 10⁻²¹ J
b) 9.17 × 10²² J
c) 8.17 × 10⁻²¹ J
d) 7.17 × 10²⁰ J
Explanation: This question is based on Kinetic Theory of gases, which describes gases as collections of tiny particles in constant random motion. The average kinetic energy of gas molecules depends directly on temperature measured in Kelvin. As temperature increases, Molecular motion becomes more energetic, increasing kinetic energy. At a given temperature, all gases have the same average kinetic energy per Molecule regardless of their type. This relationship connects microscopic particle motion with macroscopic temperature. It is a key concept in Thermodynamics and helps explain gas pressure, diffusion, and thermal behavior. The value can be determined using fundamental constants and temperature conversion principles, showing the direct link between thermal energy and Molecular motion.
Option b – 9.17 × 10²² J
A brick is pushed with a 7 N force and moves 5 m. How much work is done?
a) 25 J
b) 35 J
c) 40 J
d) 35 erg
Explanation: This question is based on the definition of work in physics. Work is said to be done when a force causes displacement in the direction of that force. The amount of work depends on the magnitude of force applied and the distance moved by the object in the direction of that force. If force and displacement are aligned, the work is maximum. This principle is widely used in mechanics to measure energy transfer during motion. It helps in analyzing how much energy is required to move objects and how machines perform mechanical tasks. Understanding work is essential for linking force, motion, and energy in physical systems.
Option b – 35 J
When a stone is thrown upward, which energy conversion occurs?
a) Kinetic energy changes to mechanical energy.
b) Potential energy changes to gravitational energy.
c) Mechanical energy changes to kinetic energy.
d) Kinetic energy changes to gravitational potential energy.
Explanation: This question is based on energy transformation during vertical motion. When a stone is thrown upward, it initially has energy due to its motion. As it rises, this energy decreases because gravity slows it down, while its height increases. The lost motion-based energy gets stored as position-based energy due to increasing height in Earth’s gravitational field. At the highest point, motion temporarily stops before the object begins to fall back down. This continuous transformation between motion and position energy illustrates the conservation of mechanical energy in ideal conditions. It is a fundamental example used to explain how energy changes form in projectile motion and gravitational systems.
Option d – Kinetic energy changes to gravitational potential energy.
Pressure of a Human Body on Sand
a) Greater while standing than when lying down
b) Less while standing than when lying down
c) Identical whether standing or lying
d) Higher while standing during the day and lower while lying at night
Explanation: This question is based on the concept of pressure, which depends on force and the area over which it is applied. When a person stands, the body’s weight is distributed over a smaller surface area compared to when lying down. Since pressure increases when the same force acts over a smaller area, standing produces greater pressure on the ground. When lying down, the contact area increases significantly, reducing the pressure exerted on the surface. This explains why objects or bodies sink more when pressure is concentrated and less when it is spread out. This principle is widely applied in understanding everyday interactions between Solid surfaces and force distribution.
Option a – Greater while standing than when lying down
Weight of an Object on a Planet with Nine Times Earth’s Gravity
a) Weight stays the same
b) Weight becomes 1 N
c) Weight increases ninefold
d) Weight decreases to one-ninth
Explanation: Weight is the force experienced by an object due to gravity, and it depends directly on the gravitational field strength of the planet. When gravity increases, the force acting on the same mass increases proportionally. This means the same object will feel heavier on a planet where gravitational acceleration is greater compared to Earth. The mass of the object remains unchanged, but the force it experiences changes with location. This distinction is important in mechanics because mass is an intrinsic property, while weight is a variable force. Understanding this helps in comparing how objects behave under different gravitational environments, such as on planets, moons, or other celestial bodies where gravity differs significantly from Earth.
Option c – Weight increases ninefold
Momentum and Kinetic Energy of a 10 kg Object Moving at 10 m/s
a) 100 N·s and 500 J
b) 100 N·s and 1000 J
c) 200 N·s and 500 J
d) 200 N·s and 1000 J
Explanation: This question is based on two fundamental physical quantities describing motion: momentum and kinetic energy. Momentum depends on both mass and velocity and represents the quantity of motion an object possesses. Kinetic energy depends on mass and the square of velocity, representing the energy due to motion. Because velocity appears differently in both expressions, the two quantities do not scale in the same way. When speed changes, kinetic energy changes more rapidly than momentum due to its squared dependence. This distinction is crucial in analyzing moving objects, collisions, and energy transformations. It helps explain why high-speed motion leads to significantly larger energy changes compared to momentum changes in mechanical systems.
Option a – 100 N·s and 500 J
Quantity That Remains Constant During Free Fall ( Class 9 Gravitation mcqs with Answers )
a) Acceleration
b) Momentum
c) Potential energy
d) Kinetic energy
Explanation: This question is based on motion under gravity when air resistance is ignored. During free fall, an object accelerates downward due to Earth’s gravitational pull. As it falls, its speed increases continuously, which means quantities related to motion and energy keep changing. Potential energy decreases while kinetic energy increases, showing continuous transformation between forms. However, one important aspect of such motion is that acceleration due to gravity remains constant near Earth’s surface. This constant acceleration is responsible for the uniformly changing velocity of the object. Understanding this helps in solving equations of motion and analyzing vertical movement where only gravitational force acts on the body.
Option a – Acceleration
Factors Affecting Acceleration Due to Gravity on Earth ( Class 9 Gravitation mcqs with Answers )
a) Mass of Earth only
b) Radius of Earth only
c) Either mass or radius of Earth
d) Both mass and radius of Earth
Explanation: Acceleration due to gravity depends on properties of the planet, not the object falling on it. It is determined by the mass of the Earth and the distance from its center, which is closely related to Earth’s radius. A larger mass increases gravitational pull, while a larger radius reduces its effect because distance weakens gravitational influence. These factors combine to define the strength of gravity at a given location. Changes in altitude or depth can also slightly alter its value. Understanding these dependencies is important in geophysics, satellite motion, and gravitational studies, as it explains why gravity is not perfectly uniform everywhere on Earth.
Option d – Both mass and radius of Earth
Mobile Phone Microphone and Speaker 1. Microphone changes sound into a mechanical signal 2. Microphone converts sound into an electrical signal 3. Speaker turns a mechanical signal into sound 4. Speaker changes an electrical signal into sound. Which options are correct?
a) 1 and 3
b) 1 and 4
c) 2 and 3
d) 2 and 4
Explanation: This question deals with energy conversion in Communication devices. A microphone converts sound energy into electrical signals by detecting vibrations and transforming them into varying electrical currents. A speaker performs the reverse process, converting electrical signals back into sound waves by vibrating a diaphragm. These conversions are essential for transmitting and reproducing sound in electronic devices. The process involves transduction, where one form of energy is converted into another suitable for processing or output. Understanding this helps in analyzing how audio devices function in Communication systems, where sound is captured, transmitted, and reproduced using electrical circuits and mechanical vibrations.
Option d – 2 and 4
Gravitational Force if the Moon’s Distance from Earth is Reduced by Half ( Class 9 Gravitation mcqs with Answers )
a) Decreases to half its original value
b) Doubles its original value
c) Remains unchanged
d) Becomes four times its original value
Explanation: This question is based on Newton’s law of gravitation, which states that gravitational force depends inversely on the square of the distance between two masses. When the distance between two objects decreases, the force between them increases significantly. If the separation becomes smaller, the attraction becomes stronger because gravitational influence grows rapidly as distance reduces. This relationship is important in understanding orbital motion and interactions between celestial bodies. It explains why changes in distance between astronomical objects can strongly affect their gravitational behavior and motion dynamics in space systems.
Option d – Becomes four times its original value
Relationship Between Mass and Weight ( Class 9 Gravitation mcqs with Answers )
a) Weight changes with location, but mass remains constant
b) Mass changes with location, but weight stays constant
c) Both weight and mass remain unchanged everywhere
d) Both weight and mass change with location
Explanation: This question distinguishes between two fundamental physical quantities. Mass is the amount of Matter in an object and remains constant regardless of location. Weight, on the other hand, is the force experienced by that mass due to gravity and depends on the gravitational field strength. Since gravity varies from place to place, weight also changes accordingly, while mass does not. This distinction is essential in physics because it helps separate intrinsic properties from force-based effects. Understanding this relationship is important in mechanics, especially when analyzing objects on different planets, satellites, or varying gravitational environments where weight changes but mass remains unchanged.
Option a – Weight changes with location, but mass remains constant
Weight of a 50 kg Person in a Lift Accelerating Upward at 1 m/s² ( Class 9 Gravitation mcqs with Answers )
a) 490 N
b) 540 N
c) 440 N
d) 50 N
Explanation: This question is based on apparent weight in accelerating systems. When a lift accelerates upward, the normal force exerted by the floor increases because it must support both the weight of the person and provide additional force for upward acceleration. This makes the person feel heavier than usual. The actual mass remains constant, but the force experienced changes due to acceleration. This situation is commonly used to understand non-inertial frames of reference where additional apparent forces appear. It is an important concept in dynamics and helps explain how acceleration affects perceived weight in elevators and other moving systems.
Option b – 540 N
Statement Incorrect for a Freely Falling Object ( Class 9 Gravitation MCQs with Answers )
a) It accelerates
b) Its momentum keeps changing
c) Its motion is affected only by gravity
d) Its motion is affected by both gravity and air resistance
Explanation: This question examines motion under gravity when air resistance is ignored. A freely falling object experiences only gravitational force, resulting in constant acceleration downward. Its velocity changes continuously, and its momentum also changes as speed increases. However, if air resistance is considered, motion is affected by both gravity and drag forces. Understanding the correct condition for free fall is essential in physics because it defines an idealized system used in kinematics. It helps distinguish between ideal motion models and real-world motion where additional forces may act on the object.
Option d – Its motion is affected by both gravity and air resistance
Situations Where Applied Force Does Negative Work ( Class 9 Gravitation MCQs with Answers )
a) Force and displacement form an angle of 135°
b) Force and displacement are parallel
c) Force and displacement are perpendicular
d) Force and displacement form an angle of 45°
Explanation: This question is based on the concept of work and the direction of force relative to displacement. Work done depends on the angle between applied force and displacement. When the force acts opposite to the direction of motion, work becomes negative because it removes energy from the system. If force acts perpendicular, no work is done, and if it acts in the same direction, work is positive. Negative work commonly occurs in situations involving friction, resistance, or braking forces where motion is opposed. This concept is important in energy analysis, helping understand how different forces either add to or reduce the mechanical energy of a system.
Option a – Force and displacement form an angle of 135°
Speed of a 2 kg Object with 100 J of Kinetic Energy ( Class 9 Gravitation MCQs with Answers )
a) 10.0 m/s
b) 11.1 m/s
c) 11.2 m/s
d) 12.1 m/s
Explanation: This question is based on the relationship between kinetic energy, mass, and velocity. Kinetic energy represents the energy an object possesses due to its motion and depends on both its mass and the square of its speed. When kinetic energy is known, the velocity of the object can be determined by rearranging the standard relation. Since velocity is squared in the expression, even small changes in energy lead to noticeable changes in speed. This relationship is widely used in mechanics to analyze moving bodies, collisions, and energy transfer systems. It also helps in understanding how energy input translates into motion in physical systems where mass remains constant. The concept is fundamental in linking energy and motion quantitatively.
Option a – 10.0 m/s
Nature of Buoyant Force on Immersed Objects ( Class 9 Gravitation MCQs with Answers )
a) Downward pressure
b) Downward force
c) Upward pressure
d) Upward force
Explanation: This question is based on fluid mechanics and the concept of buoyancy. When an object is immersed in a fluid, it experiences an upward force due to the difference in pressure between its lower and upper surfaces. This force acts opposite to gravity and is responsible for the apparent reduction in weight of objects in fluids. The magnitude of this force depends on the volume of fluid displaced and the density of the fluid. It plays a key role in determining whether an object will float or sink. This principle explains the behavior of ships, submarines, and balloons, and is fundamental in understanding fluid behavior and equilibrium conditions in liquids.
Option d – Upward force
Dimensions of the Gravitational Constant ( Class 9 Gravitation MCQs with Answers )
a) M L T⁻²
b) M L¹ T⁻²
c) M² L⁻¹ T⁻²
d) M-1 L3 T2
Explanation: This question is based on dimensional analysis of physical constants. The gravitational constant appears in Newton’s law of gravitation, which relates force between two masses to their product and the square of their separation distance. By rearranging this relation using the dimensions of force, mass, and distance, the dimensions of the gravitational constant can be derived. Dimensional analysis helps ensure consistency in physical equations and provides insight into how different physical quantities relate to each other. It is widely used in physics to verify formulas, derive relationships, and understand the fundamental nature of constants used in mechanics and gravitational studies.
Option d – M-1 L3 T2
Power Needed to Lift an 8 kg Mass 4 m in 2 Seconds (g = 10 m/s²)
a) 80 W
b) 160 W
c) 320 W
d) 640 W
Explanation: This question deals with the concept of power, which is the rate at which work is done. When an object is lifted against gravity, work is done equal to the increase in its gravitational potential energy. This work depends on mass, gravitational acceleration, and height. Power is obtained by dividing this work by the time taken. A shorter time requires higher power because the same energy is transferred more quickly. This idea is important in understanding how machines and humans perform work efficiently over time. It is widely applied in mechanical systems like cranes, elevators, and engines where energy transfer rate is a key factor in performance.
Option b – 160 W
Gravitational Forces Between Earth and Moon ( Class 9 Gravitation MCQs with Answers )
a) Earth’s gravitational pull on the Moon is stronger than the Moon’s pull on Earth
b) Moon’s gravitational pull on Earth is stronger than Earth’s pull on the Moon
c) Both forces are equal in size and direction
d) Both forces are equal in size but opposite in direction
Explanation: This question is based on Newton’s third law of motion and universal gravitation. When two bodies interact gravitationally, each exerts an attractive force on the other. These forces always occur in pairs and are equal in magnitude but opposite in direction. This means both bodies pull each other with the same strength, even though their effects may differ due to differences in mass. This principle is fundamental in understanding orbital motion and celestial interactions. It explains why the Moon orbits the Earth while both bodies still exert equal gravitational attraction on each other. This concept is essential in analyzing motion in space systems and gravitational equilibrium.
Option d – Both forces are equal in size but opposite in direction
We covered all the Class 9 Gravitation MCQs with Answers above in this post for free so that you can practice well for the exam.
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