The Potential Energy of Spring NEET Questions

Physics - Work, Energy, and Power

The Potential Energy of Spring MCQ Questions


7.
A spring with spring constant k is compressed by 1 cm, storing potential energy U. If it is further compressed by 3 cm, the change in potential energy will be:

NEET - 2021

A.
9U
B.
8U
C.
4U
D.
3U
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ANSWER :
B. 8U
8.
The potential energy stored in a spring (constant k) displaced by x from its natural length is:
A.
V(x) = kx
B.
V(x) = ½kx²
C.
V(x) = kx²
D.
V(x) = ½kx
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ANSWER :
B. V(x) = ½kx²
9.
The potential energy of a spring V(x) = kx²/2 is obtained by:
A.
Differentiating Fs = −kx with respect to x
B.
Integrating the external force F_ext = +kx over displacement from 0 to x
C.
Using Newton's second law F = ma directly
D.
Multiplying spring force by time
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ANSWER :
B. Integrating the external force F_ext = +kx over displacement from 0 to x
10.
When a spring is stretched by 10 cm, the potential energy stored is E. If the spring is stretched by 20 cm, the potential energy stored will be:

NEET - 2020

A.
2E
B.
4E
C.
8E
D.
16E
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ANSWER :
B. 4E
11.
Verify that V(x) = kx²/2 is correct by using the relation F(x) = −dV/dx:
A.
−d(kx²/2)/dx = −kx = Fs ✓ (confirms Hooke's Law)
B.
−d(kx²/2)/dx = +kx (confirms F is in direction of stretch)
C.
d(kx²/2)/dx = kx = Fs (no negative sign needed)
D.
−d(kx²/2)/dx = k (constant, not proportional to x)
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ANSWER :
A. −d(kx²/2)/dx = −kx = Fs ✓ (confirms Hooke's Law)
12.
The zero of spring potential energy is chosen at:
A.
The maximum extension xm
B.
The equilibrium position x = 0 (natural length)
C.
The midpoint between −xm and +xm
D.
Wherever PE equals kinetic energy
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ANSWER :
B. The equilibrium position x = 0 (natural length)