Unit Test (Solutions): Work and Energy

Time: 1 hour 
M.M. 30 
Attempt all questions. 
Question numbers 1 to 5 carry 1 mark each. 
Question numbers 6 to 8 carry 2 marks each. 
Question numbers 9 to 11 carry 3 marks each. 
Question numbers 12 & 13 carry 5 marks each.

Q1. What is the SI unit of work? (1 Mark)

Ans: Joule (J)

Q2. Define kinetic energy. (1 Mark)

Ans: Kinetic energy is the energy possessed by a body due to its motion.

Q3. When is work done by a force considered negative? (1 Mark)

Ans: When force and displacement are in opposite directions.

Q4. What is the gravitational potential energy of an object at height h? (1 Mark)

Ans: mgh

Q5. What is the SI unit of power? (1 Mark)

Ans: Watt (W)

Q6. Explain why no work is done when a person holds a heavy load stationary on their head. (2 Marks)

Ans: No work is done because there is no displacement of the load in the direction of the applied force.

Q7. Differentiate between kinetic and potential energy. (2 Marks)

Ans:

Kinetic energy is the energy possessed by a body due to its motion, such as a moving car. It is given by the formula ½mv².
Potential energy is the energy possessed by a body due to its position or configuration, like an object at a height. It is given by the formula mgh.

Q8. Why does a moving object possess energy? Give an example. (2 Marks)

Ans: A moving object possesses kinetic energy due to its motion. 
Example: A speeding car can do work by pushing objects it collides with.

Q9. A ball of mass 2 kg is dropped from a height of 5 m. Calculate:
(a) The potential energy of the ball at the top.
(b) The kinetic energy of the ball just before hitting the ground.
(c) What does this example prove about the total mechanical energy?

Take g = 10 m/s². (3 Marks)

Ans: (a) Potential Energy (PE) = mgh = 2 × 10 × 5 = 100 J
(b) Just before hitting the ground, all potential energy is converted to kinetic energy.
So, Kinetic Energy (KE) = 100 J
(c) This example shows that total mechanical energy (PE + KE) remains constant during free fall (in absence of air resistance), proving the law of conservation of energy.

Q10. An object of mass 5 kg is moving with a velocity of 4 m/s. Calculate its kinetic energy. What happens to its kinetic energy if the velocity is doubled? (3 Marks)

Ans: Kinetic Energy = ½mv²
= 1/2 × 5 kg × (4 m/s)²
= 1/2 × 5 × 16 = 40 J

If velocity is doubled (8 m/s):
KE = 1/2 × 5 × (8)² = 1/2 × 5 × 64 = 160 J
Hence, when velocity is doubled, kinetic energy becomes four times.

Q11. Describe how a stretched rubber band acquires potential energy. (3 Marks)

Ans: When a rubber band is stretched, work is done against its elastic forces, transferring energy to it. This energy is stored as potential energy due to its changed configuration. When released, the potential energy is converted to kinetic energy as the band returns to its original shape.

Q12. Explain the law of conservation of energy with the example of a freely falling object. (5 Marks)

Ans: Law of Conservation of Energy: Energy can neither be created nor destroyed. It only transforms from one form to another, but the total energy remains constant.
For a freely falling object:

• At the highest point, the object has maximum gravitational potential energy (mgh) and zero kinetic energy.
• As it falls, potential energy decreases as height reduces, while kinetic energy (½mv²) increases due to increasing velocity.
• The total mechanical energy (potential + kinetic) remains constant, assuming no air resistance.
• Example: A 2 kg object dropped from 10 m (g = 10 m/s²) has initial PE = 2 × 10 × 10 = 200 J. 
  At halfway (5 m), PE = 2 × 10 × 5 = 100 J, and KE = 200 J - 100 J = 100 J. 
  Total energy remains 200 J throughout.

Q13. A 20 kg object is raised to a height of 4 m and then dropped. Calculate its potential energy at the top and kinetic energy halfway down. Explain how this illustrates energy transformation. (5 Marks)

Ans: Given: m = 20 kg, h = 4 m, g = 10 m/s²

1. Potential Energy at the top:
   PE = mgh = 20 × 10 × 4 = 800 J
2. Halfway down (h = 2 m):
   PE = mgh = 20 × 10 × 2 = 400 J
   By conservation of energy, total energy = 800 J
   KE = Total energy - PE = 800 J - 400 J = 400 J

Energy Transformation: 
Initially, energy is in the form of potential energy. As the object falls, PE is converted into KE. At the halfway point, energy is equally divided between PE and KE. This shows transformation of energy without any loss, confirming the law of conservation of energy.