Free Work and Energy MCQs with Answers

21. The efficiency of a machine is

• A. always greater than 100 per cent
• B. the ratio of useful output energy to total input energy, expressed as a percentage
• C. the ratio of input to output
• D. equal to the power output

Explanation: Efficiency can never exceed 100 per cent, because energy is conserved and some is always lost to friction, sound and heat. An electric motor may reach 90 per cent while a petrol engine manages only about 25 per cent. The wasted energy is not destroyed, merely converted into forms that are not useful.

22. A machine takes in 500 J and delivers 400 J of useful output. Its efficiency is

• A. 80 per cent
• B. 125 per cent
• C. 100 per cent
• D. 20 per cent

Explanation: Dividing 400 by 500 and multiplying by 100 gives 80 per cent, with the remaining 100 J lost mainly as heat. Dividing the wrong way round gives 125 per cent, which should be recognised at once as impossible. The 20 per cent figure is the fraction wasted rather than the efficiency.

23. In a real pendulum swinging back and forth, the total mechanical energy slowly decreases because

• A. energy is destroyed
• B. energy is transferred to the surroundings as heat and sound by air resistance and friction at the pivot
• C. gravity weakens
• D. the mass of the bob decreases

Explanation: Energy is conserved overall, but the mechanical energy of the pendulum is gradually converted into thermal energy of the air and the pivot, so the amplitude decays. In an ideal frictionless case the exchange between kinetic and potential energy would continue indefinitely. Nothing is ever destroyed, which is what the conservation principle asserts.

24. A force acts on a body but does negative work. This means the force

• A. acts in the same direction as the displacement
• B. has a component opposite to the displacement, so it removes energy from the body
• C. does no work at all
• D. acts at right angles to the displacement

Explanation: Friction and air resistance always oppose the motion and therefore always do negative work, reducing the kinetic energy. A force at right angles does zero work rather than negative work, which is the distinction being tested. Gravity does negative work on a body moving upwards and positive work as it comes back down.

25. The elastic potential energy stored in a spring stretched by extension x with spring constant k is

• A. kx
• B. half kx squared
• C. kx squared
• D. half kx

Explanation: The force rises linearly from zero to kx, so the average force is half of kx and the work done is half k x squared, which is also the area under the force extension graph. This is why doubling the extension quadruples the stored energy. The formula holds only while Hooke's law applies, that is below the elastic limit.

26. A body of mass 1 kg has kinetic energy 50 J. Its speed is

• A. 5 m per second
• B. 10 m per second
• C. 50 m per second
• D. 100 m per second

Explanation: From half mv squared equal to 50, v squared is 100 and v is 10 m per second. Forgetting the factor of one half gives about 7.1, and forgetting to take the square root gives 100. Checking the units at the end is a quick guard against both slips.

27. Which of the following is NOT a renewable source of energy?

• A. Solar
• B. Wind
• C. Coal
• D. Hydroelectric

Explanation: Coal is a fossil fuel formed over hundreds of millions of years, so it is consumed far faster than it can be replaced and its combustion releases carbon dioxide. Solar, wind and hydroelectric are all replenished continuously by natural processes. Pakistan's electricity mix relies heavily on hydroelectric and thermal generation.

28. For a body sliding down a frictionless slope, the speed at the bottom depends on

• A. the length of the slope
• B. the vertical height dropped, but not on the angle of the slope
• C. the mass of the body
• D. the angle only

Explanation: Energy conservation gives half mv squared equal to mgh, so the mass cancels and only the height matters, which means a gentle ramp and a steep one of the same height give the same final speed. The gentle slope simply takes longer. Friction would break this result, since the longer path would then waste more energy.

29. The law of conservation of energy states that energy

• A. can be created when needed
• B. can be destroyed by friction
• C. can be transformed from one form to another but the total remains constant
• D. always increases in an isolated system

Explanation: Friction does not destroy energy; it converts organised kinetic energy into disordered thermal energy, which is harder to use but is still energy. Every apparent loss in mechanics is a transfer to a form outside the system being considered. Including mass as a form of energy through E equals mc squared makes the law hold in nuclear reactions too.

30. If P is the momentum of an object and m is its mass, then its kinetic energy is:

• A. P/2m
• B. P2/2m
• C. 1/2 Pm2
• D. 1/2 P2m

Explanation: Kinetic energy is half mv squared and momentum is mv, so substituting v equal to P over m gives half m multiplied by P squared over m squared, which simplifies to P squared over 2m. A quick check is that energy must rise with the square of momentum, which only the second option does. This relation is used constantly in collision and de Broglie problems.