Question

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

• A. $2M$
• B. $M$
• C. $M/2$
• D. A function of $M$ and the force constant of the spring

Answer 1

The correct option is C $M/2$

Mass of A is $m$

If mass A move to a distance $x$, then spring will stretch to $x$ value. And it will lift the mass of B

Force in the spring, $F=kx=Mg......\left(1\right)$

Kinetic energy = Potential energy

$\frac{1}{2}k{x}^2=mgx$
$kx=2mg......\left(2\right)$

From (1) and (2)

$Mg=2mg$

$m=\frac{M}{2}$

Required mass of A is $\frac{M}{2}$ , to lift mass B