A ball is let fall from a height h. It makes n collisions with the earth. After n collisions it rebounds with a velocity v_(n) and the ball rises to a height h_(n) then coefficient of restitution is given by

Options

A. `e=[(h_(n))/(h_(0))]^(1//2n)`
B. `e=[(h_(0))/(h_(n))]^(1//2n)`
C. `e=1/n sqrt(h_(n))/(h_(0))`
D. `e=1/n sqrt(h_(0))/(h_(n))`

Answer

a

Explanation

height after n rebound, `h_(n)=e^(2n)h_(0)`
`e^(2n)=h_(n)/h_(0)`
`e=[h_(n)/h_(0)]^(1//2n)`