Question

In stretching a spring by $2cm$ energy stored is given by $U$, then stretching by $10cm$ energy stored will be :

• A. $U$
• B. $5U$
• C. $\frac{U}{25}$
• D. $25U$

Answer 1

The correct option is D $25U$

Given Data $x_1=2cm$

Energy stored $U_1=U$

$x_2=10cm$

$U_2=?$

Let Extension Produced as a spring be x initially

in streched condition spring will have

potentiate energy

$U=\frac{1}{2}k{x}^2$

$k$ is spring constant $u\alpha x^2$

$\frac{u_1}{u_2}=\frac{x_1^2}{x_2^2}$

$-:u_1,2u$

$\frac{u}{u_2}=\frac{2^2}{{10}^2}\Rightarrow u_2=\frac{{10}^{2}u}{4}$

$u_2=25u$

$\therefore u_2=25u$

$AnswerisD$