Question

If a spring extends by $x$ on loading, then energy stored by the spring is (Given: $T$ is the tension in spring and $k$ is spring constant)

• A. $\frac{T^2}{4k}$
• B. $\frac{2T^2}{k}$
• C. $\frac{T^2}{2k}$
• D. $\frac{T^2}{k}$

Answer 1

The correct option is C $\frac{T^2}{2k}$

Energy stored in spring $E=\frac{1}{2}k{x}^2$
$T=kx\Rightarrow x=\frac{T}{k}$

$\therefore E=\frac{1}{2}k{\left(\frac{T}{k}\right)}^2=\frac{1}{2}\frac{T^2}{k}$