Conservation of Energy - UNSOLVED PRACTICE SET
Chapter: Work Energy and Power | Topic: Conservation of Energy
CONSERVATION OF ENERGY - UNSOLVED PRACTICE SET
Topic: Conservation of Energy
Multiple Choice Questions
Q1. The Law of Conservation of Energy states that:
- Energy can be created from nothing if enough force is applied
- The total energy of an isolated system always remains constant
- Kinetic energy and potential energy are always equal
- Energy is lost whenever work is done
Q2. A pendulum swings from its highest point to the lowest point. At the lowest point:
- Total energy is zero
- PE is maximum, KE is zero
- KE is maximum, KE is zero
- Both KE and PE are equal
Q3. When a stone falls from a cliff, which energy transformation occurs?
- KE → PE
- PE → KE
- PE → Heat
- KE → Sound
Q4. A ball is dropped from a height h. Just before it hits the ground (ignoring air resistance), its total mechanical energy is:
- Only KE = mgh
- Only PE = mgh
- Total mechanical energy = mgh (same as at the top)
- Zero
Q5. Energy is said to be 'dissipated' when:
- It is converted from PE to KE
- It transforms into heat, sound, or other non-useful forms
- It is stored in a spring
- Gravity does work on an object
Q6. Which of the following is the best example of chemical energy converting to kinetic energy?
- A light bulb glowing
- A car engine burning petrol to move the car
- A solar panel generating electricity
- A waterfall generating power
Short Answer Questions
Q7. State the Law of Conservation of Energy. Give one example from daily Indian life where you can observe this law in action.
Q8. Explain the energy transformation that occurs when a pendulum swings from one extreme to the other and back. At which point is PE maximum? At which is KE maximum?
Q9. A stone of mass 1 kg is dropped from a height of 10 m. Using conservation of energy and g = 10 m/s², find its velocity just before hitting the ground. Show the energy conversion.
Q10. Why does a ball dropped on the floor not bounce back to its original height? Where does the 'missing' energy go? Does this violate the Law of Conservation of Energy?
Q11. A hydroelectric power plant like the one at Tehri Dam converts one form of energy to another. Trace the energy transformations from rain falling on mountains to electricity reaching your home.
Q12. Explain the term 'mechanical energy'. Write the formula for total mechanical energy and state when it remains conserved.
Long Answer Questions
Q13. Using the example of a freely falling body, prove the Law of Conservation of Mechanical Energy. Your proof must include:
(a) expressions for PE and KE at the point of release (top),
(b) expressions at an intermediate height h₂,
(c) expressions just before hitting the ground,
(d) showing that KE + PE = constant = mgh at all three points, and
(e) stating under what condition this proof holds (no air resistance).
Q14. A roller-coaster at an amusement park starts from rest at the top of a 40 m high ramp. (Ignore friction.)
(a) Calculate the total energy at the top (mass of cart + passengers = 500 kg, g = 10 m/s²).
(b) Using conservation of energy, find the speed at the bottom.
(c) At a midpoint 15 m above ground, find both the KE and PE.
(d) Verify that KE + PE at the midpoint equals the total energy at the top.
(e) In a real roller-coaster, why doesn't it reach exactly 40 m on the next rise?
Q15. Trace and explain all energy transformations in the following scenarios:
(a) A child eats food and then plays cricket — from digestion to hitting a six.
(b) The sun shining on a solar water heater on an Indian rooftop.
(c) A wind turbine generating electricity in Rajasthan's Thar Desert.
(d) A person speaking on a mobile phone.
(e) For each, identify where energy is 'lost' (converted to less useful forms) and whether the Law of Conservation of Energy is violated.
Numerical / Application-Based Problems
Q16. A 2 kg ball is released from rest from a height of 25 m. (g = 10 m/s²) At a height of 10 m above the ground, calculate:
(a) the gravitational PE,
(b) the KE (using energy conservation: KE = total E − PE),
(c) the velocity at that height.
(d) Verify your answer by checking that KE + PE = initial PE.
Q17. A pendulum bob of mass 0.3 kg swings from rest at a height of 0.5 m above the lowest point. (g = 10 m/s²)
(a) Calculate the PE at the highest point.
(b) Calculate the velocity at the lowest point using conservation of energy.
(c) At a height of 0.2 m, find the velocity.
(d) Calculate the KE and PE at h = 0.2 m and verify that their sum equals the original PE.
Q18. In a hydroelectric dam, water of mass 10,000 kg falls through a height of 50 m. (g = 10 m/s²)
(a) Calculate the PE of the water at the top.
(b) If 90% of the PE is converted to electrical energy, calculate the electrical energy produced.
(c) How many 100 W bulbs can this energy keep lit for 1 hour? (1 hour = 3600 s; Energy = Power × Time)