Question

A block of mass $m$ starts from rest and slides down a frictionless semi-circular track from height $h$ as shown. When it reaches the lowest point of the track, it collides with a stationary piece of putty also having mass $m$. If the block and the puttty stick together and continue to slide, the maximum height that the block-putty system could reach is:

• A. $\frac{h}{4}$
• B. $\frac{h}{2}$
• C. $h$
• D. independent of $h$

Answer 1

The correct option is A $\frac{h}{4}$

The velocity of block just before hitting the putty (by energy conservation)

${K.E}_i+{P.E}_i={K.E}_f+{P.E}_f\Rightarrow 0+mgh=\frac{1}{2}m{v}^2\Rightarrow v=\sqrt{2gh}$

Let the common velocity of both block and putty be v'

At collision momentum balance:

$mv=m{v}^{\prime }+m{v}^{\prime }\Rightarrow \sqrt{2gh}=2v^{\prime }\Rightarrow v^{\prime }=\sqrt{\frac{gh}{2}}$

Again applying energy conservation (both block and putty at max height)

${K.E}_i+{P.E}_i={K.E}_f+{P.E}_f\Rightarrow \frac{1}{2}2m{v^{\prime }}^2=2mg{h}^{\prime }\Rightarrow \frac{1}{2}\frac{gh}{2}=g{h}^{\prime }\Rightarrow h^{\prime }=h/4$