Potential Energy MCQ Quiz - Objective Question with Answer for Potential Energy - Download Free PDF

The correct answer is 2 kJ.

CONCEPT:

• Potential energy: The energy of any object due to its position with respect to a reference point is called potential energy. It is denoted by PE.

Potential energy is given by:

PE = m g h.

Here, PE is the Potential Energy, m is the mass, g is the acceleration due to gravity, and h is the height at which the object is placed

CALCULATION:

Given that: 

Mass (m) = 10 Kg

Height (h) = 20 m

P.E. = 10 x 10 x 20

P.E.= 2000 J

 P.E. = 2 kJ

• Kinetic energy: The energy due to the motion of the object is called kinetic energy. 
  • Kinetic energy (KE) = 1/2 (mv²)
  • Where m is mass and v is velocity. 
• Since the object is stationary (at rest) so the velocity is zero. Hence the kinetic energy of the object will be zero.
• Only the potential energy of the object will be there at the height.

Calculation:

(A) Force is zero at x = -a, 0, a. Oscillation about x = ±a for energy U₀ / 4 → (p), (q), (r), (t)

(B) Force is zero at x = 0. It's attractive near x = 0 → (q), (s)

(C) Force is zero at x = -a, 0, a. Potential well around x = 0 → (p), (q), (r), (s)

(D) Force is zero at x = -a and x = a. Oscillation possible around x = -a for U₀ / 4 → (p), (r), (t)

Solution:

When B is displaced towards the wall 1 by a distance x, spring S₁ is compressed by x and S₂ is unstretched. The total energy of the spring-mass system is:

E₁ = (1/2) × k × x²

When B returns and moves a maximum distance y towards wall 2, spring S₂ is compressed by y and S₁ is unstretched. The total energy of the system is:

E₂ = (1/2) × (4k) × y²

Since there is no friction and masses are negligible, total mechanical energy is conserved. Therefore:

(1/2) × k × x² = (1/2) × 4k × y²

⇒ kx² = 4k y² ⇒ x² = 4 y² ⇒ x = 2y ⇒ y / x = 1/2

Concept:

The problem involves two balls rolling down ramps of different heights. The first ramp has a height of h, and the second ramp has a height of h. According to the principles of energy conservation and kinematics, the speed of the balls when they reach the bottom will depend on the potential energy they convert into kinetic energy as they roll down the ramp. The potential energy at the top is proportional to the height, and this energy is completely converted into kinetic energy (assuming no friction). The speed of the balls at the bottom of the ramp will be determined by the square root of the height from which they fall.

Calculation:

v_ii = √(2g(2h)) = √(4gh) = 2√(gh)

For the ball on ramp (i), the potential energy at height h is converted into kinetic energy at the bottom. The velocity at the bottom is given by:

vi = √(2gh)

For the ball on ramp (ii), the potential energy at height h is converted into kinetic energy. The velocity at the bottom is given by:

vii = √(2g(h)) = √(2gh)

From this, we can see that Both balls will have the same speed after hitting the ground.

The correct answer is Option 3.

Explanation:

Potential Energy and Dead State:

• Potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. For a mechanical system, potential energy typically refers to the energy stored due to the position of objects within the system, such as the height of an object above the ground in a gravitational field.
• The dead state of a system, on the other hand, is a condition where the system is in complete equilibrium with its surroundings. This means that there is no net exchange of energy or matter with the environment. In this state, the system possesses no capacity to do work. Essentially, the system is in a state of minimum energy and maximum entropy.

Why Zero Velocity and Minimum Potential Energy?

• In the dead state, the system is in equilibrium, meaning there is no motion or change occurring.
• Therefore, the system must have zero velocity. Velocity indicates movement and kinetic energy, which would imply that the system could still do work, contradicting the definition of the dead state.
• Moreover, the system must have minimum potential energy.
• Minimum potential energy means that the system is in its most stable configuration.
• If the potential energy were higher, the system would have the capacity to change its state to achieve a lower energy configuration, which again implies the potential to do work.
• Hence, for the system to be truly in a dead state, it must be at the lowest possible energy level, both kinetically and potentially.

The correct answer is 2 kJ.

CONCEPT:

• Potential energy: The energy of any object due to its position with respect to a reference point is called potential energy. It is denoted by PE.

Potential energy is given by:

PE = m g h.

Here, PE is the Potential Energy, m is the mass, g is the acceleration due to gravity, and h is the height at which the object is placed

CALCULATION:

Given that: 

Mass (m) = 10 Kg

Height (h) = 20 m

P.E. = 10 x 10 x 20

P.E.= 2000 J

 P.E. = 2 kJ

• Kinetic energy: The energy due to the motion of the object is called kinetic energy. 
  • Kinetic energy (KE) = 1/2 (mv²)
  • Where m is mass and v is velocity. 
• Since the object is stationary (at rest) so the velocity is zero. Hence the kinetic energy of the object will be zero.
• Only the potential energy of the object will be there at the height.

CONCEPT:

• Kinetic energy (KE): The energy possessed by a body by virtue of its motion is called kinetic energy.

\(KE = \frac{1}{2}m{v^2}\)

Where m = mass of the body and v = velocity of the body

• Potential energy (PE): The energy possessed by a body by virtue of its position or configuration is called potential energy.

\(PE = mgh\)

Where, m = mass of the body, g = acceleration due to gravity, and h = height of the body

• Conservation of energy: According to the conservation of energy, energy can’t be created or destroyed, it can only transform from one form to another.
• The total energy of the system remains constant i.e. the sum of kinetic energy + potential energy remains constant.

EXPLANATION:

• In a free fall, the total energy (T.E.) is constant that is T.E = kinetic energy + potential energy.
• When the objects fall down, their potential energy converted into kinetic energy. So the potential energy decreases and the kinetic energy increases.
• Since the total energy is constant so that the increase in kinetic energy brings down the potential energy value and vice versa.

CONCEPT:

• Potential energy is defined as the energy stored due to change in position relative to others, stresses within itself, or many factors.
  • The potential energy (U) = m g h [where m= mass of body, g= acceleration due to gravity, h = distance from the ground].
  • If the height of a body increases from the ground its energy also increases and vice versa.

• Under free fall where gravity is the sole influence on the body, the total energy remains the same
• Potential energy gets converted into kinetic energy.
• Under free fall, the potential energy keeps on decreasing and kinetic energy keeps on increasing.
• This is also in confirmation with the law of conservation of energy

EXPLANATION:

• From the above-given explanation, we can see that at the highest position, the kinetic energy of the particle is zero and the potential energy is maximum. Therefore option 1 is correct.
• Whereas at the lowest position, potential energy becomes zero and kinetic energy is maximum as the ball about to hit the ground

 CONCEPT:

• Potential Energy: Potential energy is the energy stored within an object, due to the object's position, arrangement or state.
• It can be given by:

P. E. = m × g × h

Where P = potential energy, m = mass, g = acceleration due to gravity, h = heigh of the object.

CALCULATION:

Given that: the mass of body 50 kg, Height covered 10 m, g = 10 m/s².

Formula:

Potential energy = mass × acceleration due to gravity(g) × height covered

P. E. = m × g × h = 50 × 10 × 10 = 5000 Joule.

So option 2 is correct.

CONCEPT:

• Conservative force: A force is conservative if the work done by the force in displacing an object from one point to another point is independent of the path followed by the object and depends only on the endpoints.
• Electrostatic forces, gravitational forces, elastic forces, magnetic forces, etc and are the examples of a conservative force.

• Non-conservative forces: A force is said to be non-conservative if work done by or against the force in moving a body from one position to another, depends on the path followed between these two positions.
• Example:  Frictional force, Viscous force, Airdrag, etc.

EXPLANATION:

• If a body of mass m lifted to height h from the ground level by a different path, then the work done in each case will be the same. Therefore, in conservative force work done by the force in displacing an object from one point to another point is independent of path followed by the object and depends only on the endpoints.

• If a body is moved from position A to another position B on a rough table, work done against frictional force shall depend on the length of the path between A and B and not only on the position A and B. Therefore, in non-conservative force work done by or against the force in moving a body from one position to another, depends on the path followed between these two positions.

CONCEPT:

• Potential energy: The energy of an object due to its position is called potential energy. It is denoted by PE.
  • Mathematically potential energy can be written as 
  • P.E of object =  m g h

​​Where m = mass of an object, g = acceleration due to gravity, and h = height

CALCULATION:

We are given,

m = 1 kg, g = 10 m/s², h = 5 metres

PE = 1 × 10 × 5 = 50 J

Hence option 1 is correct.

Option 3 is correct.

CONCEPT:

• Kinetic energy (KE): The energy possessed by a body by virtue of its motion is called kinetic energy.

\(KE = \frac{1}{2}m{v^2}\)

Where m = mass of the body and v = velocity of the body

• Potential energy (PE): The energy possessed by a body by virtue of its position or configuration is called potential energy.

\(PE = mgh\)

Where, m = mass of the body, g = acceleration due to gravity and h = height of the body

• Conservation of energy: According to the conservation of energy, energy can’t be created or destroyed, it can only transform from one form to another.
  • The total energy of the system remains constant i.e. the sum of kinetic energy + potential energy remains constant.

EXPLANATION:

• When the object is falling from the height then the potential energy of the object will decrease and kinetic energy will increase.
• But according to conservation of energy principle, the sum of the KE and PE (total energy) will remain the same. So option 3 is correct.

• The correct answer is Option 4 i.e 100 J.

CONCEPT:

• Work is said to be done by a force when the body is displaced actually through some distance in the direction of the applied force.
• Since the body is being displaced in the direction of F, therefore work done by the force in displacing the body through a distance s is given by:

\(W = \vec F \cdot \vec s\)

• Potential energy (PE): The energy possessed by a body by virtue of its position or configuration is called potential energy.
  • When an object is lifted from the ground, work is done against the force of gravity, since the force of gravity always acts downwards.

\(PE = mgh\)

Where, m = mass of the body, g = acceleration due to gravity and h = height of the body

CALCULATION:

Given that: 

Mass (m) = 5 kg

Height (h) = 2 m

Here the work done by Ravi will get converted into the potential energy of the dumbbell at that height.

Work done (W) = m x g x h 

⇒ W = 5 x 10 x 2

⇒ W = 100 J

Hence option 4 is correct.

The correct option is: 2

CONCEPT:

• Potential energy: The energy of an object due to its position is called potential energy. It is denoted by PE.
  • Mathematically potential energy can be written as 
  • P.E of object =  m g h

​​Where m = mass of an object, g = acceleration due to gravity, and h = height

CALCULATION:

Initial height = H

Initial Potential energy = PE₁ = m g H

Final height (h) = H × 80 % = 0.8 H

Final potential energy = PE₂ = m g h = 0.8 m g H

Ratio = PE₂/PE₁ = (0.8 m g H)/(m g H) = 4/5

Option 2 is correct, i.e. 400 Joule.

CONCEPT:

• Potential energy (PE): The energy possessed by a body by virtue of its position or configuration is called potential energy.

\(PE = mgh\)

Where, m = mass of the body, g = acceleration due to gravity and h = height of the body

CALCULATION:

Given that:

Mass of the object, m = 20 kg,
displacement (height), h = 2 m, and
acceleration due to gravity, g = 10 m s^–2.

Potential Energy = mgh = 20×10×2 = 400 J.

So option 2 is correct.