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. `theta(pi)/(4)`
B. `(pi)/(4)ltthetalt(pi)/(4)`
C. `(pi)/(2)ltthetalt(3pi)/(4)`
D. `(3pi)/(4)ltthetaltpi`

Answer

C

Explanation

when the string rotates by `90^(@)`, the speed of ball is
`v'=v^(2)=2gL=3gL`
`v'=sqrt(3gL)`
`v_(1)^(2)=v^(2)-2gL(1+cos alpha)`
`2gL(1+cosalpha)=(3v^(2))/(4)=(3)/(4)xx5gL`