Question

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

• A. V/25
• B. 5 V
• C. V/5
• D. 25 V

Answer 1

Answer: (D)

$U=\frac{1}{2}\left(\frac{YA}{L}\right)l^2$
$\therefore U\propto l^2$
$\frac{U_2}{U_1}={\left(\frac{l_2}{l_1}\right)}^2={\left(\frac{10}{2}\right)}^2=25$
$\Rightarrow U_2=25U_1$
i.e., potential energy of the spring will be $25V$.