Work Energy and Power - Result Question 21
24. When a long spring is stretched by $2 cm$, its potential energy is $U$. If the spring is stretched by $10 cm$, the potential energy stored in it will be
(a) $25 U$
(b) $U / 5$
(c) $5 U$
(d) $10 U$
[2003]
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Answer:
Correct Answer: 24. (a)
Solution:
- (a) If $k$ be the spring constant, then
$U=\frac{1}{2} \times k \times(2)^{2}=2 k$
$U _{\text{final }}=\frac{1}{2} \times k \times(10)^{2}=50 k$
$\Rightarrow \frac{U}{U _{\text{final }}}=\frac{2 k}{50 k}=\frac{1}{25}$
$\Rightarrow U _{\text{final }}=25 U$
