Hailstorms are observed to strike the surface of a frozen lake at an angle of `30^(@)` with the vertical and rebound at an angle of `60^(@)` with vertical. Assuming the contact to be smooth, the coefficient of restitution is

Options

A. `e = (1)/(sqrt(3))`
B. `e = (1)/(3)`
C. `e = sqrt(3)`
D. e = 3

Answer

B

Explanation

Components of velocity before and after collisionparalleltotheplaneareequal,So
`v sin 60^(@) = u sin 30^(@) " "….(1)`
Components of velocity normal to the plane are related to each other
`V cos 60^(@) = e u (cos 30^(@)) " ".........(2)`
`rArr cot 60^(@) = e cot 30^(@) rArr e = (cos 60^(@))/( cot 30^(@))`
`rArr e = ((1)/(sqrt(3)))/(sqrt(3)) rArr e =(1)/(3)`