Question

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

Answer 1

`v=sqrt(2gL)`
Let at angle`theta " " v^(2)=(v)/(2)=sqrt((gL)/(2))`
`(1)/(2)mv^(2)=(1)/(2)mv^(2)+mgR(1- costheta)`
`cos theta= (1)/(4)`
`(pi)/(4)ltthetalt(pi)/(2)`