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 the fixed horizontal floor as shown in figure. The spring is initially unstretched and the spring-block system is released from rest in the shown position. At the instant speed of block is maximum, the magnitude of force exerted by spring on the block is

• A. $\frac{mg}{2}$
• B. $mg$
• C. zero
• D. None of these

Answer 1

The correct option is B $mg$

The speed of block is maximum when it is at its mean position. Hence $v=v_{\text{max}}$ when $a=0$
$\Rightarrow$At this instant the block is in equilibrium i.e $F_{\text{net}}=0$
When speed is maximum let the compression in spring is $x$
$\Rightarrow kx=mg$
$\therefore$The spring exerts a force equal to $mg$ on the block.