Conservation of Energy Important Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. Which of the following is not true?

1. Energy cannot be destroyed
2. The energy of an open system can be varied
3. Energy cannot be created
4. Energy cannot be transformed

Ans. The correct answer is d. Energy cannot be transformed

Explanation: Energy cannot be created or destroyed, only transformed. In open systems, energy can vary due to ongoing matter and radiation exchanges.

Ques. The energy possessed by an object because of its motion is termed

1. kinetic energy
2. solar energy
3. potential energy
4. nuclear energy

Ans. The correct answer is a. kinetic energy

Explanation: The energy possessed by a body due to its motion is known as kinetic energy.

Ques. For a freely falling body, which of the following quantities will not change?

1. Total potential energy
2. Total mechanical energy
3. Total kinetic energy
4. None of the above

Ans. The correct answer is b. Total mechanical energy

Explanation: The velocity of a body falling freely under the influence of gravity increases with the decrease in height. As a result, there is a decrease in potential energy but an increase in kinetic energy. However, according to the law of conservation of energy, the total mechanical energy, i.e. the sum of potential and kinetic energy, always remains constant.

Ques. The law of conservation of energy does not apply to mechanical systems as they require energy input to keep working.

1. True
2. False

Ans. The correct answer is b. False

Explanation: The law of conservation of energy applies to mechanical systems, however, it may not apply to a "machine" that requires continuous power input to operate since it becomes an open system.

Ques. Which of the following statements is true?

1. Energy cannot be created but only destroyed
2. Energy can be created and destroyed
3. Energy can neither be created nor destroyed
4. Energy cannot be destroyed but only created

Ans. The correct answer is c. Energy can neither be created nor destroyed

Explanation: Energy is a conserved quantity which means it cannot be created nor destroyed but it can change from one form to another.

Ques. What is the dimensional formula of energy?

1. [ML²T^-1]
2. [ML²T^-2]
3. [MLT^-2]
4. [MLT^-1]

Ans. The correct answer is b. [ML²T^-2]

Explanation: The dimensional formula of energy is [ML²T^-2]

Ques. Fire is a form of

1. thermal energy
2. kinetic energy
3. gravitational energy
4. solar energy

Ans. The correct answer is a. thermal energy

Explanation: Thermal energy is the result of the temperature of an object being carried in the form of heat from a source of higher temperature to an area or object of lower temperature through mechanisms such as conduction, convection, or radiation.

Ques. When a shutter of a dam opens, _____ energy is transformed into kinetic energy.

1. Electric energy
2. Chemical energy
3. Heat energy
4. Potential energy

Ans. The correct answer is d. Potential energy

Explanation: When a shutter of a dam opens, the potential energy of the stored water in the dam is transformed into kinetic energy.

Ques. The maximum potential energy in a roller coaster is at

1. somewhere during the descent
2. somewhere during the climb
3. the top of the steep climb
4. the lowest point after the climb

Ans. The correct answer is c. the top of the steep climb

Explanation: The potential energy of a body is directly proportional to its height from the surface. Hence the potential energy of the roller coaster is maximum at the top of the steep climb.

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Short Answers Questions [2 Marks Questions]

Ques. What is the conservation of energy?

Ans. Conservation of energy states that energy cannot be created or destroyed but it can change from one form to another form. In an isolated system, the total energy of the body will remain constant.

Ques. What is energy?

Ans. Energy is a fundamental property of matter that can be transferred or transformed. It is the ability to do work, and it can manifest itself in various forms, including heat, light, and kinetic energy (the energy of motion). Energy is a conserved quantity, meaning that it can neither be created nor destroyed, but only changed from one form to another.

Ques. What is kinetic energy?

Ans. The energy possessed by a body due to its motion is known as kinetic energy.

Let a body of mass m move with velocity v, then its kinetic energy is given by

K.E. = 1/2 mv²

Ques. Define potential energy.

Ans. The energy possessed by a body due to its change in its position or change in shape is called potential energy.

Let a body of mass m is taken to a height h from the surface of the earth, then the potential energy stored in the body is given by

P.E. = mgh

Ques. What is meant by mechanical energy?

Ans. The total kinetic and potential energy of a body is called mechanical energy. It represents the energy of the body due to its motion, position, or both.

Ques. Give an example of energy conversion from chemical energy to kinetic energy.

Ans. The chemical energy contained in petrol is converted into kinetic energy by a car engine, which moves the vehicle forward. When petrol is consumed in the combustion chambers of an engine, it produces heat and gases. The heat causes the gases to expand, pushing on the pistons of the engine. This piston action is turned into the rotational motion of the crankshaft, which rotates the wheels and propels the vehicle. 

Ques. Does gravity conserve energy?

Ans. Gravity is infinite in the sense that it never stops functioning. Gravity will always exist as long as the planet has mass. However, because gravity is a force rather than an energy, its limitless nature cannot be used to extract unlimited or any energy.

Ques. What is the relation between kinetic energy and linear momentum?

Ans. The relation between kinetic energy and linear momentum is given by

\(p = \sqrt{2m(K.E)} \)

Where

• p is the linear momentum of the body
• m is the mass of the body
• K.E is the kinetic energy

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Long Answers Questions [3 Marks Questions]

Ques. What are the examples of the law of conservation of energy?

Ans. The following are the examples of the law of conservation of energy

• The chemical energy of the batteries is converted into electrical energy in a torch, which is then converted into light and heat energy.
• Waterfalls from a height on turbines at hydroelectric power plants. This, in turn, causes the turbines to rotate and create electricity. As a result, the potential energy of water is turned into turbine kinetic energy, which then transforms into electrical energy.
• Electrical energy is transformed into sound energy in a loudspeaker.
• Sound energy is converted into electrical energy in a microphone.
• Mechanical energy is converted into electrical energy in a generator.

Ques. A body is thrown vertically upward from the surface of the earth with 10 J of kinetic energy. What will be the potential energy at the highest point of its journey?

Ans. Given the kinetic energy of the body on the surface of the earth is 10 J. Also the potential energy of the body on the surface is zero, therefore

The total energy at the surface of the earth is the sum of kinetic energy and potential energy i.e.

E_i = K_i + P_i

⇒ E_i = 10 + 0 = 10 J

The velocity of the body at the highest point is zero, hence the kinetic energy of the body at the highest point is zero. 

Let P_f be the potential energy of the body at its highest point, then total energy at the highest point is given by

E_f = K_f + P_f

⇒ E_f = 0 + P_f

⇒ E_f = P_f

According to the law of conservation of energy, E_i = E_f

⇒ P_f = 10 J

Ques. Explain the energy conservation of a pendulum.

Ans. The swing of a simple pendulum is upward and downward. 

• When the pendulum stops shortly at the height of its swing, the kinetic energy becomes zero, and all of the energy components of the system are completely related to potential energy. 
• When the pendulum knob falls, the potential energy is converted back to kinetic energy. 
• The total of kinetic and potential energy is always constant.

Ques. What is the difference between kinetic and potential energy?

Ans. The following are the differences between kinetic energy and potential energy

Ques. What is the effect of friction on the conservation of energy?

Ans. Friction slows down most of the physical processes, especially motion (it continually dissipates energy). 

• The sum of thermal, potential, and kinetic energy is the ideal conserved quantity. 
• When a box slides down a ramp, for example, potential energy is converted to kinetic energy. 
• When friction causes the box's motion to come to a stop, the kinetic energy is converted into thermal energy. 
• No new energy is produced or destroyed, as stated by the conservation law. 
• It only changes the form (from potential energy to kinetic energy to thermal energy).

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Very Long Answers Questions [5 Marks Questions]

Ques. A girl in a swing is 2.5 m above the ground at the maximum height and at 1.5 m above the ground at the lowest point. What is the maximum velocity of her swing? (Take g = 10 m/s²)

Ans. Given

• The distance of the highest point, h₁ = 2.5 m
• The distance of the lowest point, h₂ = 1.5 m

The kinetic energy of the girl at the highest point, K_i = 1/2 mv²

Since the velocity of the body at the highest point is zero, therefore total kinetic energy at the highest point will also become zero.

K_i = 1/2 x m x 0 = 0

The potential energy of the girl at the highest point is given by

P_i = mgh₁ = m x 10 x 2.5 = 25m

Total energy at the highest point, E_i = K_i + P_i

⇒ E_i = 0 + 25m = 25m

Let v be the velocity of the girl at a height of 1.5 m, then 

The kinetic energy of the girl, K_f = 1/2 mv²

The potential energy of the girl, P_f = mgh²

⇒ P_f = m x 10 x 1.5 = 15m

The total energy of the girl, E_f = K_f + P_f

⇒ E_f = 1/2 mv² + 15m

According to the law of conservation of energy, E_i = E_f

⇒ 25m = 1/2 mv² + 15m

⇒ v = 4.47 m/s

Hence the maximum velocity of her swing is 4.47 m/s.

Ques. A spring gun of spring constant 90 N/cm is compressed 12 cm by a ball of mass 16 g. If the trigger is pulled, what will be the velocity of the ball?

Ans. Given

• The spring constant of the spring gun, k = 90 N/cm = 90 x 10² N/m
• Distance through with the spring is compressed, x = 12 cm = 12 x 10^-2 m
• The mass of the ball, m = 16 g = 16 x 10^-3 kg

The potential energy of the spring gun when it is compressed is given by

P.E = 1/2kx²

⇒ P.E = 1/2 x 90 x 10² x (12 x 10^-2)² = 64.8 J

Let v be the velocity of the ball when the triggered is pulled, therefore kinetic energy of the ball is given by

K.E = 1/2 mv²

⇒ K.E = 1/2 x 16 x 10^-3 x v² = 8 x 10^-3 x v²

According to the law of conservation of energy,

Loss in the PE of the spring = gain in KE of the ball

⇒ 64.8 = 8 x 10^-3 x v²

⇒ v² = 8100

⇒ v = 90 m/s

Ques. Prove the law of conservation of energy in case of a freely falling body.

Ans. Let us consider a ball of mass m is dropped from height H.

Law of Conservation of Energy

At point A:

• The kinetic energy of the ball, KE = 0
• The potential energy of the ball, PE = mgH

The total mechanical energy of the ball at point A, E_A = 0 + mgH = mgH

At point B:

Potential energy of the ball, PE = mg (H - x)

Using the equation of motion, v² = u² + 2as, we get

v² = 0 + 2(-g)(-x) = 2gx

Now, kinetic energy, KE = 1/2 mv² = 1/2 m(2gx) = mgx

Total mechanical energy, E_B = mg (H - x) + mgx = mgH

At point C:

Potential energy, PE = 0

Using the equation of motion, v² = u² + 2as, we get

v² = 0 + 2(-g)(-H) = 2gH

Now, kinetic energy, KE = 1/2 mv² = 1/2 m(2gH) = mgH

Total mechanical energy, E_C = 0 + mgH = mgH

Total mechanical energy during the whole path is conserved. Hence the law of conservation of energy proved.

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