Question

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

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

Answer 1

Answer: (B)

Extension of spring $=x$, fension on spring $=T$ and spring constant $=k .$ Now extension of spring $x=\frac{T}{k}$ and energy stored by the spring
$E=\frac{1}{2} \times k x^{2}=\frac{1}{2} \times k \times\left(\frac{T}{k}\right)^{2}=\frac{1}{2} \times k \times \frac{T^{2}}{k^{2}}=\frac{T^{2}}{2 k}$.