In the given figure, a smooth parabolic wire track lies in the x y -plane (vertical). The shape of track is defined by the equation y = x 2 . A ring of mass m which can slide freely on the wire track, is placed at the position A ( 1 , 1 ) . The track is rotated with constant angular speed ω such that there is no relative slipping between the ring and the track, the value of ω is

Question

In the given figure, a smooth parabolic wire track lies in the x y -plane (vertical). The shape of track is defined by the equation y = x 2 . A ring of mass m which can slide freely on the wire track, is placed at the position A ( 1 , 1 ) . The track is rotated with constant angular speed ω such that there is no relative slipping between the ring and the track, the value of ω is, g 2, g, 2 g, 2 g

MARKS App · Accepted Answer

N cos ⁡ θ = m g And N sin ⁡ θ = m ω 2 r ∴ tan ⁡ θ = ω 2 r g ...(i) Given y = x 2 ∴ d y d x = 2 x Or tan ⁡ θ = 2 × 1 = 2 ...(ii) From above equations, we get ω = 2 g r = 1 m

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