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. `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 1

Correct Answer - B
From given condition, `v = sqrt(5gL)`
From energy conservation

`(m(v//2)^(2))/(2) -(mv^(2))/(2) = -mgL(1-cos theta)`
or `cos theta = -(7)/(8)`
The value of `theta` given in option `(4)` can only have a value of `theta` as comouted above, so `(4)` is correct.