If potential energy of a spring is V on stretching it by 2, cm , then its potential energy when it i

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8.Mechanical Properties of Solids

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If the potential energy of a spring is $V$ on stretching it by $2\, cm$, then its potential energy when it is stretched by $10 \,cm$ will be

A

$V/25$

B

$5V$

C

$V/5$

D

$25V$

Solution

(d) $U = \frac{1}{2}\left( {\frac{{YA}}{L}} \right)\,{l^2}$ $\Rightarrow$ $U \propto {l^2}$

$\frac{{{U_2}}}{{{U_1}}} = {\left( {\frac{{{l_2}}}{{{l_1}}}} \right)^2} = {\left( {\frac{{10}}{2}} \right)^2} = 25$ $\Rightarrow$ ${U_2} = 25{U_1}$

i.e. potential energy of the spring will be $25 \,V$

Standard 11

Physics

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