The Potential Energy of Spring NEET Questions

Physics - Work, Energy, and Power
The Potential Energy of Spring

The Potential Energy of Spring MCQ Questions


7.
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
8.
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)
9.
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)
10.
A spring is stretched by 0.2 m. Then it is compressed by 0.2 m. Ratio of PE in the two cases is:
A.
1 : 2 (compression stores more energy)
B.
2 : 1 (extension stores more energy)
C.
1 : 1 (same PE for equal magnitude displacement)
D.
Cannot be determined
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ANSWER :
C. 1 : 1 (same PE for equal magnitude displacement)
11.
Work done by an external agent in slowly compressing a spring (k = 600 N/m) by 0.05 m is:
A.
0.75 J
B.
1.5 J
C.
0.375 J
D.
3 J
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ANSWER :
A. 0.75 J
12.
A spring (k = 400 N/m) block moves from xᵢ = 0.1 m to xf = 0.3 m. Work done BY spring force is:
A.
+16 J
B.
−16 J
C.
−4 J
D.
4 J
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ANSWER :
B. −16 J
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