Oscillations - Result Question 25
28. The potential energy of a long spring when stretched by $2 cm$ is $U$. If the spring is stretched by $8 cm$, the potential energy stored in it is
(a) $8 U$
(b) $16 U$
(c) $U / 4$
(d) $4 U$
[2006]
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Answer:
Correct Answer: 28. (b)
Solution:
- (b) The potential energy of a spring $=\frac{1}{2} k x^{2}$
$U=\frac{1}{2} k \cdot(2)^{2}=4 \times \frac{1}{2} k$
For $x=8 cm$,
Energy stored $=\frac{1}{2} k \cdot(8)^{2}=64 \times \frac{1}{2} k$
$=64 \times \frac{U}{4}=16 U$
