A particle moves from rest at A on the surface of a smooth circular cylinder of radius r as shown - Physics -

Question

A particle moves from rest at A on the surface of a smooth circular
cylinder of radius r as shown At B it leaves the cylinder
The equation relating α and β is

(a) 3 sin α = 2 cos β (b) 2 sin α = 3 cos
â€‹β (c) 3 sin â€‹β =
2 cos α (d) 2 sin â€‹β = 3 cos α

Vaibhav T. · Accepted Answer

Dear Student,

As the normal force does no work on the particle, its energy is conserved
K+Up1=K+Up20+mgR cosα=12mv22+mgR sinβv22=2gRcosα-sinβAt P2, the normal force exerted by the surface vanishes, leaving the radial component of the particle's weight, mg sinβ, as the instantaneous centripetal force
Then, by newton's second law,mg sinβ=mv22Rmg sinβ=mR2gRcosα-sinβsinβ=2cosα-2sinβsinβ=23cosα

A particle moves from rest at A on the surface of a smooth circular cylinder of radius r as shown. At B it leaves the cylinder. The equation relating α and β is (a) 3 sin α = 2 cos β (b) 2 sin α = 3 cos ​β (c) 3 sin ​β = 2 cos α (d) 2 sin ​β = 3 cos α

A particle moves from rest at A on the surface of a smooth circular cylinder of radius r as shown. At B it leaves the cylinder. The equation relating α and β is

(a) 3 sin α = 2 cos β (b) 2 sin α = 3 cos β (c) 3 sin β = 2 cos α (d) 2 sin β = 3 cos α