An elastic ball of mass 'm' is suspended from a fixed point 'O' by an inextensible string of length `2m`. A small particle of mass m moving downward at angle of `37^(@)` with the vertical hits the ball with `v_(0)`. The coefficient of restitution for collision is `4//5`. the velocity of the particle `v_(0)` such that ball just comoplete on revolution after the collision.

Options

A. `(170)/(27) m//s`
B. `(85)/(27) m//s`
C. `(680)/(27) m//s`
D. `(340)/(27) m//s`

Answer

D

Explanation

`v_(1)` and `v_(2)` are the velocity after the collision.
`mv_(0)sin 37^(@) = mv_(1)sin 37^(@) + mv_(2)`....(i)
`e = (4)/(5) = (v_(2) cos 53^(@) - v_(1))/(v_(0))` ...(ii)
From (i) and (ii)
`v_(2) = (27)/(34)v_(00 = sqrt5gl`
`(27)/(34)v_(0) = 10`
`rArr v_(0) = (340)/(27) m//sec`