Question

A mass M is suspended as shown in $Fig.6.384$. The system is in equilibrium. Assume pulleys to be massless. K is the force constant of the spring.
The extension produced in the spring is given by

• A. $4Mg/K$
• B. $Mg/K$
• C. $2Mg/K$
• D. $3Mg/K$

Answer 1

The correct option is C $2Mg/K$

Since when maximum extension takes place the body is not in equilibrium but momentarily at rest only before raising up we use conservation of energy principle.
Loss in $PE$ of block$=$ increase the inelastic potential energy of spring$.$

$\begin{array}{c}Let{x}_{m}bemaximumextension\\ thenMg{x}_m=\frac{1}{2}K{x}_m^2\\ x_m=\frac{2Mg}{K}\end{array}$

Hence,

option $\left(C\right)$ is correct answer.