A particle is released on a vertical smooth semicircular track from point X so that, O X makes angle θ from the vertical (see figure). The normal reaction of the track on the particle vanishes at the point Y where O Y makes an angle ϕ with the horizontal. Then

Question

A particle is released on a vertical smooth semicircular track from point X so that, O X makes angle θ from the vertical (see figure). The normal reaction of the track on the particle vanishes at the point Y where O Y makes an angle ϕ with the horizontal. Then, sinϕ = 2 3 cosθ, sinϕ = 3 4 cosθ, sinϕ = 1 2 cosθ, sinϕ = cosθ

MARKS App · Accepted Answer

m g R cos θ - R sin ϕ = 1 2 m V 2 . . . . . . . (1) On losing contact N =0⇒ m g sinϕ = m V 2 R . . . . . . (2) ⇒ m g R cosθ - sinϕ = 1 2 m g R sinϕ ⇒ 2 cos θ = 3 sinϕ

Search any question & find its solution

Looking for more such questions to practice?