Question

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. 5 V
• C. V/5
• D. 25 V

Answer 1

Answer: (D)

$U=\frac{1}{2}\left(\frac{Y A}{L}\right) l^{2}$
$\therefore U \propto l^{2}$
$\frac{U_{2}}{U_{1}}=\left(\frac{l_{2}}{l_{1}}\right)^{2}=\left(\frac{10}{2}\right)^{2}=25$
$\Rightarrow U_{2}=25 U_{1}$
i.e., potential energy of the spring will be $25\, V$.