A bob of mas `M` is suspended by a massless string of length `L`. The horizontal velocity `v` at position `A` is just sufficient to make it reach the point `B`. The angle `theta` at which the speed of the bob is half of that at `A`, satisfies.
.

Options

A. `theta = (pi)/4`
B. `pi/4 lt theta lt pi/2`
C. `pi/2 lt theta lt (3pi)/(4)`
D. `(3pi)/4 lt theta lt pi`

Answer

D

Explanation

`v = sqrt(5 gL)`
`(v/2)^2 = v^2 - 2gh implies h = L (1 - cos theta)`
Solving the three equation, we get
`cos theta = -7/8 "or" theta = cos^(-1)(-7/8) = 151^@`.