Question

When a small mass $m$ is suspended at lower end of the elastic wire having upper end fixed with ceiling. There is loss in gravitational potential energy. let it be x, due to extension of wire, mark correct option,

• A. The lost energy can be recovered
• B. The lost energy can be irrecoverable
• C. only $\frac{x}{2}$ amount of energy recoverable
• D. only $\frac{x}{3}$ amount of energy recoverable

Answer 1

Answer: (C)

only $\frac{x}{2}$ amount of energy recoverable

Work energy theorem
$\begin{array}{c}{w}_{spring}+w_{gravity}+w_{loss}=0\\ -\frac{1}{2}k{x}^2+mgx+w_{loss}=0\\ -\frac{1}{2mgx}+mgx+w_{loss}=0\\ w_{loss}=-\frac{mgx}{2}\end{array}$

Since there is a loss so not recoverable
half of it is lost rest is recoverable