A bob of mass M is suspended by a massless string of length L. The horizonta 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. (a) `theta=pi/4`
B. (b) `pi/4ltthetaltpi/4`
C. (c) `pi/2ltthetalt(3pi)/(4)`
D. (d) `(3pi)/(4)ltthetaltpi`

Answer

D

Explanation

`v=sqrt(5gL)`
`(v/2)^2=v^2-2ghimpliesh=L(1-costheta)`
Solving the three equations, we get
`cos theta=7/8` or `theta=cos^-1(-7/8)=151^@`