CHAPTER NO 04 WORK ENERGY AND POWER PRACTICE MCQS SOLUTION BY PHYSICS INN-ABDULLAH 

 

Topic: 4.1 Work Done by a Constant Force

Answer Key with Hints/Solutions

1. (b) Sol:  from .
2. (c) Sol: .
3. (b) Sol: Work is the scalar dot product of two vectors ().
4. (c) Sol: As force does not vary with displacement, the graph is a horizontal straight line.
5. (c) Sol: Displacement , so work done .
6. (d) Sol: For ,  is negative, so work done is negative.
7. (b) Sol: Area of rectangle/curve under  vs  equals .
8. (c) Sol: Perpendicular component  contributes zero work ().
9. (c) Sol: The upward normal force is perpendicular to the horizontal displacement ().
10. (b) Sol: Only the component along displacement () performs work.
11. (b) Sol: Friction acts opposite to displacement (), so .
12. (a) Sol: .
13. (c) Sol: .
14. (a) Sol: .
15. (c) Sol: . 

    Topic: 4.2 Work Done by a Variable Force

    Answer Key with Hints/Solutions

1. (c) Sol: To handle non-constant forces, the interval  is made small enough that the force vector remains nearly constant during that interval.
2. (b) Sol: Taking the limit as  converts the sum of rectangular areas into the exact area under the curve.
3. (c) Sol: The work done by a variable force equals the area under the  versus  curve.
4. (c) Sol: As a rocket leaves Earth, gravity varies inversely as the square of distance, serving as a classic example of variable force.
5. (b) Sol:  only applies when force  and angle  are constant throughout displacement .
6. (c) Sol: As interval length , the sum of approximate rectangle areas equals the exact area under the curve.
7. (a) Sol: Elastic force in a spring varies directly with displacement (), so doubling stretch doubles force.
8. (b) Sol: The work done in a small interval is .
9. (c) Sol: For variable forces, exact work is determined by evaluating the area under the force-displacement curve.
10. (b) Sol: .
11. (b) Sol: Linear increase forms a triangle on the - graph, so .
12. (b) Sol: .
13. (a) Sol: .
14. (b) Sol: .
15. (b) Sol: .

    Topic: 4.3 Conservative and Non-Conservative Forces

    1. (c) Sol: Gravitational force is conservative; work done by it is independent of path.
    2. (b) Sol: By definition, work done by a conservative force along a closed path is zero ().
    3. (b) Sol: Frictional force, air resistance, and propulsion forces are non-conservative.
    4. (a) Sol: The space surrounding Earth where its gravitational force acts on a mass is its gravitational field.
    5. (c) Sol: Gravity is conservative, so .
    6. (a) Sol: Non-conservative forces perform work that depends directly on the path length.
    7. (c) Sol: Gravitational work depends only on initial and final positions (), not on the path.
    8. (b) Sol: For horizontal steps, gravity acts vertically down, so angle  and .
    9. (c) Sol: Friction is non-conservative, so work done over a round trip depends on total distance and is non-zero.
    10. (b) Sol: Air resistance and rocket propulsion are non-conservative forces.
    11. (b) Sol: The normal force acts perpendicular to the surface/motion vector at every point, so .
    12. (b) Sol: .
    13. (b) Sol: .
    14. (c) Sol: Perimeter . .
    15. (a) Sol: .

        Topic: 4.4 Power

        1. (b) Sol: .
        2. (b) Sol: Since , .
        3. (c) Sol: Kilowatt-hour is a commercial unit of electrical energy ().
        4. (c) Sol: .
        5. (b) Sol: ; if , then .
        6. (b) Sol: .
        7. (b) Sol: By definition, .
        8. (b) Sol: .
        9. (b) Sol: The motor does work against gravity at a rate  to lift the elevator at constant speed.
        10. (c) Sol: .
        11. (a) Sol: .
        12. (b) Sol: .
        13. (c) Sol: .
        14. (a) Sol: .
        15. (a) Sol: Energy .

        Topic: 4.5 Energy 

        1. (b) Sol: Energy is defined as the capacity of a body to do work.
        2. (b) Sol: Mechanical energy exists in two main forms: kinetic energy (due to motion) and potential energy (due to position/state).
        3. (c) Sol: Potential energy due to compressed or stretched state of a spring is elastic potential energy.
        4. (c) Sol: Absolute potential energy reference zero is set at infinity () where gravitational force becomes zero.
        5. (b) Sol: Absolute potential energy equation is .
        6. (b) Sol: As  increases,  becomes less negative, which means the absolute potential energy increases.
        7. (a) Sol: Work done by friction  equals the initial kinetic energy .
        8. (b) Sol:  assumes constant , but for large distances force varies as .
        9. (b) Sol: Small steps  ensure gravitational force  can be taken as constant over each step.
        10. (c) Sol: By work-energy conservation, work done by friction brings car to rest, absorbing its kinetic energy.
        11. (b) Sol: Solar energy reaching Earth in 10 days exceeds energy stored in all terrestrial fossil fuels.
        12. (b) Sol: .
        13. (b) Sol: . If , then
        14. (a) Sol: Absolute P.E. at surface .
        15. (a) Sol: .

            Topic: 4.6 Escape Velocity

            1. (b) Sol: Escape velocity is the speed required to completely leave Earth's gravitational influence.
            2. (b) Sol: Equating  into  yields .
            3. (b) Sol: .
            4. (a) Sol: Moon has the smallest escape speed () among the listed bodies.
            5. (c) Sol:  depends only on gravitational constant , planet mass , and planet radius .
            6. (b) Sol: Initial  equals Increase in .
            7. (c) Sol: Mass  of the object cancels out in .
            8. (b) Sol: Moon's mass  and radius  are much smaller, leading to a smaller ratio  in .
            9. (c) Sol: At , initial  provides enough energy to overcome gravitational attraction completely.
            10. (b) Sol: Light gas molecules (like hydrogen) achieve higher thermal speeds at a given temperature, making them exceed low escape velocities more readily.
            11. (b) Sol: ; if , then .
            12. (c) Sol: .
            13. (a) Sol: .
            14. (a) Sol: .
            (a) Sol: .

            Topic: 4.7 Work-Energy Theorem

            1. (b) Sol: Work-energy theorem states that net work done equals change in kinetic energy ().
            2. (a) Sol: .
            3. (a) Sol: From , solving for  gives .
            4. (b) Sol: Doing work against resistance extracts energy, causing kinetic energy to decrease.
            5. (b) Sol: Since , if , then , so  increases.
            6. (b) Sol: Constant velocity means .
            7. (b) Sol: The work-energy theorem is valid generally for both constant and variable forces.
            8. (c) Sol: .
            9. (a) Sol: Net force along slope is , so net work is .
            10. (b) Sol: Brakes exert retarding force opposite to displacement (), doing negative work to reduce .
            11. (c) Sol: Since velocity is constant (), the net work done by all forces combined is zero by the work-energy principle.
            12. (a) Sol: .
            13. (b) Sol: .
            14. (a) Sol: . Since , .
            15. (a) Sol: .

                Topic: 4.8 Interconversion of Potential Energy and Kinetic Energy

                1. (c) Sol: In a closed conservative system (no friction), total mechanical energy .
                2. (a) Sol: By conservation of mechanical energy, Loss in  Gain in .
                3. (b) Sol: In a resistive medium, total initial potential energy splits into kinetic energy and work against friction ().
                4. (b) Sol: .
                5. (c) Sol:  and .
                6. (a) Sol: During upward motion, initial  goes into increasing elevation () and overcoming drag friction.
                7. (a) Sol: Loss in  equals Gain in .
                8. (b) Sol: Since , .
                9. (a) Sol: Descending height reduces potential energy while accelerating the car, converting  to .
                10. (b) Sol: At maximum height, instantaneous velocity  (), so energy is entirely potential.
                11. (b) Sol: Air drag converts part of the initial potential energy into thermal work rather than kinetic energy.
                12. (a) Sol: .
                13. (b) Sol: .
                14. (b) Sol: .
                15. (a) Sol: .