Question

In the figure, the ball $A$ is released from rest when the spring is at its natural (unstretched) length. For the block $B$ of mass $M$ to leave contact with the ground at some stage, the minimum mass of $A$ must be

• A. $2M$
• B. $M$
• C. $\frac{M}{2}$
• D. $\frac{M}{4}$

Answer 1

Answer: (C)

The spring will exert maximum force when the ball is at its lowest position. If the ball has descended through a distance $x$ to reach the position.
$\operatorname{mgx}=\left(\frac{1}{2}\right) K x^2$ or $x=\frac{2 m g}{k} \ldots .$ .....(i)
For block $B$ to leave contact spring force, $Kx=Mg$ .....(i)
Comparing equations (i) and (ii), $m=\frac{M}{2}$