A heavy particle is attached to one end of a string 1m long whose other end is fixed at O. It is projected from it lowest position horizontally with a velocity V:

Options

A. If `V^(2)gt 5` g the particle will describe complete circular motion in the vertical plane
B. If `V^(2)=3.5` g the tension in the string will become zero after the string has turned through `120^(@)`
C. If `V^(2) =2` g, the tension in the string becomes zero the velocity of the particle also becomes zero
D. If `V^(2)=g` the velocity of the particle becomes zero after the string turns through `60^(@)`

Answer

A, B, C, D

Explanation

`-mgl(1-costheta)=1/2mv^(2)-1/2mv^(2).......(1)`
`T-mgcostheta=(ml^(2))/l.........(2)`
`V^(2)=(2-3costheta)`
(A)`theta=pi,V^(2)=5gl`hence true
(B) `3.5=2-3costheta,costheta=-1/2 Rightarrowtheta=120^(@)`hence true
(C) `2=2-3costheta, costheta=0,thetaRightarrow pi//2` hence true
(D) `1=2-3costheta,costheta=1/3, theta gt 60^(@)` hence true