A small sphere of mass 1 kg is moving with a velocity `(6hat(i)+hat(j))ms^(-1)`. It hits a fixed smooth wall and rebound with velocity `(4hat(i)+hat(j))ms^(-1)`. The coefficient of restitution between the sphere and the wall is

Options

A. `(3)/(2)`
B. `(2)/(3)`
C. `(9)/(16)`
D. `(4)/(9)`

Answer

(B)

Explanation

Impulse `=` Change in momentum `= 1(4hat(i) + hat(j)) - 1 (6hat(i) + hat(j)) = -2hat(i)`
Which is perpendicular to the wall.
Component of initial velocity along `hat(i) = 6hat(i) rArr` Speed of approach `= 6 m//s`
Similarly speed of separation `= 4 ms^(-1) rArr e = (4)/(6) = (2)/(3)`