Rotational Motion Question 118
Question: A ball collides with a fixed inclined plane of inclination $\theta $ after falling through a distance$h$ ? If it moves horizontally just after the impact, the coefficient of restitution is
Options:
A) $\tan \theta $
B) ${{\tan }^{2}}\theta $
C)${{\cot }^{{}}}\theta $
D) ${{\cot }^{2}}\theta $
Show Answer
Answer:
Correct Answer: B
Solution:
[b]Writing coefficient of restitution equation
$e=\frac{v _{2}-v _{1}}{u _{1}-u _{2}}=\frac{0-v\sin \theta }{-v _{0}\cos \theta -0}=\frac{v}{v _{0}}\tan \theta $
The velocity of ball will remain unchanged in the direction of sloping surface (common tangent)
$\Rightarrow v _{0}\sin \theta =v\cos \theta $
$\Rightarrow \frac{v}{v _{0}}=\tan \theta $
$\Rightarrow e={{\tan }^{2}}\theta .$
