Oscillations Ques 24
24. 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
[2006]
(a) $8 U$
(b) $16 U$
(c) $U / 4$
(d) $4 U$
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Answer:
Correct Answer: 24.(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 $ $U$
BETA
