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Potential Energy & Equilibrium

Practice Questions:

Question 1: easy

A cubical vessel of height 1 m is full of water. The minimum work done in taking water-out from vessel will be

1. 5000 J

2. 10000 J

3. 5 J

4. 10 J

View Answer

As side length of cubical tank is 1 m. Volume is 1 m³. Volume of water in 1 m³ is 1000 lit and mass will be 1000 kg.

Height of center of mass of the tank will be 1/2 m.

Potential Energy = 1000 ×10 × 1/2 = 5000 J

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Question 2: easy

Select correct statement regarding stable equilibrium

1. Potential energy of body is minimum in stable equilibrium

2. Slope of potential energy versus position graph is zero at stable equilibrium

3. A restoring force acts on the body when it is slightly displaced from its stable equilibrium position

4. All of these

View Answer

All the statements are true regarding stable equilibrium

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Question 3: easy

If potential energy between electron and proton at a distance r is given by U =-(ke²/3r³), then force acting is

1. F = ke²/r²

4. F = ke²/r

View Answer

Force F = - dU/dr = d ((ke²/3r³))/dr = ke²/r^4

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Question 4: easy

A particle with constant total energy \( E \) moves in one dimension in a region where the potential energy is represented by \( U(x) \). The speed of the particle is zero where:

1. \( \frac{d^2U(x)}{dx^2} = 0 \)

2. \( \frac{dU(x)}{dx} = 0 \)

3. \( U(x) = E \)

4. \( U(x) = 0 \)

View Answer

Total mechanical energy of a particle is the sum of its kinetic energy and potential energy: \( E = K + U(x) \). When the speed of the particle is zero, its kinetic energy \( K = 0 \), which gives \( E = U(x) \).

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