Question

If a spring extends by $x$ on loading, then the energy stored by the spring is (Given $T$ is the spring force and $K$ is force constant)

• A. $\frac{2x}{T^2}$
• B. $\frac{T^2}{2K}$
• C. $\frac{2K}{T^2}$
• D. $\frac{T^2}{2x}$

Answer 1

The correct option is B $\frac{T^2}{2K}$

Tension $T=kx\Rightarrow x=\frac{T}{k}$
Energy stored $U=\frac{1}{2}k{x}^2=\frac{1}{2}k{\left(\frac{T}{k}\right)}^2=\frac{T^2}{2k}$