A ball collides with an inclined plane of inclination `theta` after falling through a distance h. if it moves horizontal just after the impact, the coefficient of restitution is

Options

A. `tan^(2)theta `
B. `cot^(2)theta `
C. `tan theta `
D. `cot theta`

Answer

A

Explanation

Let velocity of the ball just before impact is u in the vertically downward direction . Let v is the velocity of ball in the horizontal direction just after the impact as shown in figure .

Components of velocities along and perpendicular to teh palne are shown in figure . No force acts on the ball along the surface hence its velocity in tis direction remains unaffected .
`v cos theta = u sin theta " " ....(i)`
There is collision perpendicular to the surface . If e is coefficient of restitution the we can write the following :
` v sin theta = eu cos theta " "...(ii)`
Dividing the equations (i) and (ii) we get
`(cos theta )/(sin theta ) = (sin theta )/(e cos theta ) rArr e = tan ^(2) theta ` .