250+ TOP MCQs on The Potential Energy of a Spring | Class 11 Physics

Physics Multiple Choice Questions on “The Potential Energy of a Spring”.

1. The potential energy possessed by a spring is also known as _____
a) Elastic potential energy
b) Extensive potential energy
c) Compressive potential energy
d) Deflection potential energy

Answer: a
Clarification: The potential energy stored in a spring is the consequence of its elastic property and hence it is also termed “elastic potential energy”. It can be stored when the spring is extended or compressed.

2. How much should a spring of indefinite length be compressed to have a potential energy equivalent to a ball of mass 6 kg raised to a height of 120 m above the ground? Let the spring have a stiffness of k = 100 N/m and assume g = 10 m/s².
a) 6m
b) 12m
c) 20m
d) 144m

Answer: b
Clarification: PE of ball = m x g x h
= 6 x 10 x 120
= 7200 J
PE of spring = 1/2 x k x d²
Given;
PE of ball = PE of spring
7200 = 1/2x k x d²
= 1/2 x 100 x d²
d² = 144
d = 12 m.

3. Assume a spring extend by “d” due to some load. Let “F” be the spring force and “k’ the spring constant. Then, the potential energy stored is _____
a) 2d/F²
b) F²/2k
c) 2k/T²
d) F²/2d

Answer: b
Clarification: F = k*d
PE = 1/2*k*d²
= 1/2*F*d
= 1/2*F*F/k
= F²/2k.

4. A spring of length 1m has two cars connected to both of its ends. The two cars move towards eachother such that the spring is compressed to 0.5m. If the spring constant is 500 N/m, what is the elastic potential energy stored?
a) 125 J
b) -125 J
c) 62.5 J
d) -62.5 J

Answer:c
Clarification: PE = 1/2*k*d²
= 1/2 x 500 x (-0.5) ²
= 62.5 J.
The elastic potential energy is positive even for negative displacement.

5. What is the increase in potential energy storage when the compression distance is doubled in a spring obeying Hooke’s law?
a) No increase
b) 100% increase
c) Cannot be determined
d) 4 times

Answer: d
Clarification: PE = 1/2 x k x d²
The elastic potential energy stored is directly proportional to the square of the compression. Hence, a two-fold increase in compression will result in potential energy storage to increase by four times.

6. The elastic potential energy varies linearly with displacement.
a) True
b) False

Answer: b
Clarification: PE = 1/2 x k x d²; where d = Displacement
Equation of parabola: y = 4x²
By comparing the two equations, we can conclude that the elastic potential energy varies parabolically with displacement and not linearly.