Question

A pendulum consisting of a small sphere of mass m, suspended by a inextensible and massless string of length 1 , is made to swing in a verticle plane. If the breaking strength of the string is 2 mg, then the maximum angular amplitude of the displacement from the verticle can be
A. `90^(@)`
B. `60^(@)`
C. `30^(@)`
D. `0^(@)`

Answer 1

Correct Answer - B
`T=mg(3-2 cos theta)`
`2 mg=mg[3-2 costheta]`
`2=3-2 cos theta`
`2-3=-2 cos theta`
`-1=-2 cos theta`
`-1=-2 cos theta`
` cos theta =(1)/(2)`
`theta = cos^(-1)((1)/(2))=60^(@)`