Question

A spring of force constant $k$ extends by a length $x$ on loading. If $T$ is the tension in the spring then the energy stored in the spring is

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

Answer 1

Answer: (A)

Energy stored in a spring is given by
$\mathrm{U}=\left(\frac{1}{2}\right){\mathrm{kx}}^2$ ..........(1)
Where $k$ is the spring constant
Now, applying Hooke's law, we have
Tension, $T=kx$ (in magnitude)
$\Rightarrow$ extension $x=\frac{T}{k}$
Substituting the value in equation (1), we get
$U=\frac{1}{2}\frac{T^2}{k}$ .