Question

Consider the situation shown in figure. Initially the spring is unstretched when the system is released from rest. Assuming no friction in the pulley, the maximum elongation of the spring is

• A. $\frac{m g}{k}$
• B. $\frac{2 m g}{k}$
• C. $\frac{3 m g}{k}$
• D. $\frac{4 m g}{k}$

Answer 1

Answer: (B)

$\Delta K+\Delta U_{g}+\Delta U_{s}=0$
$0+\left(-m g x_{\max }\right)+\frac{1}{2} k x_{\max }^{2}=0$
$\Rightarrow \frac{1}{2} k x_{\max }^{2}=m g x_{\max }$
$\Rightarrow x_{\max }=\left(\frac{2 m g}{k}\right)$.