A ball released from a certain height strikes the ground after 2 second. After bouncing from the ground it rises to the highest point in 1 second. What is the coefficient of restitution?

Options

A. 0.3
B. 0.4
C. 0.5
D. 0.6

Answer

C

Explanation

Let m and m be the masses of the balls A and B. Let `u_(1), u_(2)` and `v_(1),v_(2)` be their initial and final velocities respectively.

It is given that B is at rest, or `u_(2) = 0` and A is brought to rest after collision i.e., `v_(1) = 0 `
Their initial K.E. `(K_(i) ) = (1)/( 2) m u_(1)^(2) ` `( :' u_(2) =0 )` and final K.E. `(K_(f)) = (1)/(2) mv_(2)^(2) ` `( :' v_(1) =0)`
Loss in K.E. `(1)/(2) m u_(1)^(2) - (1)/( 2) mv_(2)^(2)`
`:. ( u_(1)^(2))/( 2) = v_(2)^(2)` or `v_(2) = ( u_(1))/( sqrt(2)) ` `:. (v_(2))/( u_(1)) = ( 1)/( sqrt(2))`
`:. e = (v_(2)-v_(1))/(u_(1)-u_(2)) = (v_(2))/( u_(1)) =(1)/( sqrt(2))`