Question

A small block of mass $m$ is fixed at upper end of a massless vertical spring of spring constant $K=\frac{4mg}{L}$ and natural length ${}^{\prime }10L^{\prime }.$ The lower end of spring is free and is at a height $L$ from fixed horizontal floor as shown. The spring is initially unstressed and the spring-block system is released from rest in the shown position.

As the block is coming down, the maximum speed attained by the block is:

• A. $\sqrt{gL}$
• B. $\sqrt{3gL}$
• C. $\frac{3}{2}\sqrt{gL}$
• D. $\sqrt{\frac{3}{2}gL}$

Answer 1

Answer: (C)

At the instant block is in equilibrium position, its speed is
maximum and compression in spring is $x$ given by
$kx=mg$ ......(1)
From conservation of energy
$mg(L+x)=\frac{1}{2}k{x}^2+\frac{1}{2}m{v}_{\max }^2$ .......(2)
from (1) and (2) we get
$v_{\max }=\frac{3}{2}\sqrt{gL}$.