A small sphere is given vertical velocity of magnitude `v_0=5ms^-1` and it swings in a vertical plane about the end of a massless string. The angle `theta` with the vertical at which string will break, knowing that it can withstand a maximum tension equal to twice the weight of the sphere, is

Options

A. (a) `co s^-1 (2)/(3)`
B. (b) `cos^-1(1/4)`
C. (c) `60^@`
D. (d) `30^@`

Answer

B

Explanation

`v^2=v_0^2+2glcos theta`
`T=mg cos theta+(mv^2)/(l)`
Given `T=2mg`
`2mg=mg cos theta+m/l(v_0^2+2glcos theta)_(mg cos theta)`
`impliescos theta=1/4`