Question

A ball is dropped from height ${}^{\prime }{h}^{\prime }$ as shown. The collision is perfectly inelastic. Select the correct alternative(s)

• A. The speed of the combined blocks just after collision is $\sqrt{2gh}$
• B. The speed of the combined blocks just after collision is $\left(\frac{m}{M+m}\right)\sqrt{2gh}$
• C. The amplitude of oscillations of the systems i s$\frac{mg}{k}$
• D. The amplitude of oscillations of the systems i s$\frac{mg}{k}{(1+\frac{2hk}{(M+m)g})}^{1/2}$

Answer 1

The correct option is B The speed of the combined blocks just after collision is $\left(\frac{m}{M+m}\right)\sqrt{2gh}$

The momentum will remain conserved for the following. For the velocity just after collision, change in position $\Delta x$ will be zero.

The velocity of the ball when it hits the block can be calculated as follows,

$mgh=\frac{1}{2}m{v}^2$

$v=\sqrt{2gh}$

Using the principle of conservation of momentum

$m\left(\sqrt{2gh}\right)+M\left(0\right)=\left(m+M\right)V^{\prime }$

$V^{\prime }=\frac{m}{m+M}\left(\sqrt{2gh}\right)$