question_answer

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

A) \[\tan \,\theta \] 

B) \[{{\tan }^{2}}\,\theta \]

C)  \[{{\cot }^{{}}}\,\theta \]        

D) \[{{\cot }^{2}}\,\theta \]

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) \[\Rightarrow {{v}_{0}}\sin \theta =v\cos \theta \] \[\Rightarrow \frac{v}{{{v}_{0}}}=\tan \theta \] \[\Rightarrow e={{\tan }^{2}}\theta .\]