A bullet ofmass m is fired with a velocity `10m//s` at angle `theta` with horizontal. At the hightest point of its trajectory, it collsides head-on with a bob of mass `3m` suspended by a massless string of length `2//5m` and gets embedded in the bob. After th collision the string moves through an angle of `60^(@)`.
The angle `theta` is

Options

A. `53^(@)`
B. `37^(@)`
C. `45^(@)`
D. `30^(@)`

Answer

(B)

Explanation

Velcoity of combined mass just after collision
`m (10 cos theta) = 4 mv rArr v = (5)/(2) cos theta`
But from energy conservation `(1)/(2)(4m)v^(2) = 4mgl(1 - cos 60^(@))`
`rArr v = sqrtgl = (5)/(2)cos theta rArr = (2)/(5) sqrtgl = (2)/(5) sqrt(10 xx (2)/(5)) = (4)/(5) rArr theta = 37^(@)`