A particle is attached with a string of length `l` which is fixed at point `O` on an inclined plane what minimum velocity should be given to the particle along the incline so that it may complete a circle on inclined plane `(` plane is smooth and initially particle was resting on the inclined plane . `)`

Options

A. `sqrt(5gl)`
B. `sqrt((5gl)/(2))`
C. `sqrt((5sqrt(3gl))/(2))`
D. `sqrt(4gl)`

Answer

B

Explanation

The side view of circular motion is as shown `:`

`T+mg sin theta = ( mv^(2))/(R)`
and by energy conservation `:`
`(1)/(2)mv_(i)^(2)=(1)/(2)mv^(2)+mg2R ( sin theta )`
for `v_(i)` to be minimum, `v` is minimum and hence `T=0`
`rArr v_(i)^(2)=5gR, sin theta`
`rArr v_(i)")"_(min)=sqrt((5gl)/(2)) Ans. `