Question

In the figure, the ball $P$ is released from rest, when the spring is at its natural length. For the block $Q$ of mass $2m_0$ to leave contact with ground at some stage, the minimum mass of $P$ must be

• A. $m_0$
• B. $2m_0$
• C. $m_0/2$
• D. $m_0/4$

Answer 1

The correct option is A $m_0$

For the block Q to leave contact with the surface the normal force has to be zero.

Hence weight is balanced by spring force.

$\therefore 2m_{o}g=kx$

That means that the block P has descended by a distance x, hence the decrease in gravitational energy of block P is stored in the elastic energy of the spring.

Hence

$mgx=\frac{1}{2}k{x}^2$

Hence $mg=\frac{kx}{2}$

Putting this value of $kx$ in the above equation gives a us $m=m_o$