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  4. A spring when stretched by 2 mm its potential energy becomes 4J. If it is stretched by 6 mm its potential energy becomes.

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Q. A spring when stretched by $2 \,mm$ its potential energy becomes $4J$. If it is stretched by $6 \,mm $ its potential energy becomes.

Work, Energy and Power

Solution:

$u=\frac{1}{2} k x^{2}$
$\Rightarrow u \propto x^{2} $
$\Rightarrow \frac{u_{1}}{u_{2}}=\left(\frac{2}{6}\right)^{2}$
$\therefore u_{2}=u_{1} \times \frac{36}{6}=4 \times 9=36\, J$