A pendulum consisting of a small sphere of mass m suspended by aninextensible and massless string of length l is made to swing in a vertical plane. If the breaking strength of the string is 2 mg, then the maximum angular amplitude of the displacement from the vertical can be

Options

A. `0^(@)`
B. `60^(@)`
C. `60^(@)`
D. `90^(@)`

Answer

C

Explanation

Here mass of the bob = m
length of pendulum = l
Let at any instant the amplitude = `theta`
Then according to conservation of energy K.E. = P.E.
`(1)/(2)mv^(2)=mg(l-lcostheta)`
`mv^(2)=2mgl(1-costheta)`
Equation of motion is `T-mg=(mv^(2))/(l)`
or `T=mg+(mv^(2))/(l)`
`T=mg+2mg(1-costheta)`
or `2mg=mg+2mg-2mgcostheta`
or `2mg costheta=mgorcostheta=(1)/(2)`
`therefore theta=60^(@)`