Rotational Motion Question 116
Question: A block of mass $m$ starts from rest and slides down a frictionless semi-circular track from a 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 putty stick together and continue to slide, the maximum height that the block-putty system could reach is
Options:
A)$h$ /4
B)$h$ /2
C)$h$
D)independent of $h$
Show Answer
Answer:
Correct Answer: B
Solution:
[b]
$v _{0}=\sqrt{2gh}$
before collision.
Apply conservation principle of momentum,$mv _{0}=(m+m)u$
$\therefore u=\frac{v _{0}}{2}$
Applying conservation principle of momentum,
$\frac{1}{2}(2m)u^{2}=2mgh'$
$\therefore h’=\frac{u^{2}}{2g}\Rightarrow h’\Rightarrow =\frac{v^{2} _{0}}{4g}$
$h’=\frac{2gh}{4g}\Rightarrow h’=\frac{h}{2}$
