Question

A ball of mass $m$ is attached to the lower end of a light vertical spring of force constant $k$. The upper end of the spring is fixed. The ball is released from rest with the spring is at its natural length. The ball comes to rest momentarily after descending through a distance $y$. At this position, acceleration of the ball is

• A. Zero
• B. $g$ downward
• C. $g$ upward
• D. $2g$ upwards

Answer 1

The correct option is C $g$ upward


Since non-conservative forces are absent,
$K_i+U_i=K_f+U_f$
$0+0=0+\frac{1}{2}k{y}^2-mgy$
$\Rightarrow y=\frac{2mg}{k}$
FBD at f.
$\Rightarrow ky-mg=ma$
$k\left[\frac{2mg}{k}\right]-mg=ma$
$\Rightarrow a=g,upwards.$