A uniform thin hemispherical shall is kept at rest and in equilibrium on an inclined plane of angle of inclination θ = 30 o as shown in figure. If the surface of the inclined plane is sufficiently rough to prevent sliding then the angle α m

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A uniform thin hemispherical shall is kept at rest and in equilibrium on an inclined plane of angle of inclination θ = 30 o as shown in figure. If the surface of the inclined plane is sufficiently rough to prevent sliding then the angle α made by the plane of hemisphere with inclined plane is:

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Correct answer: D. 60 o

O is the centre of mass of the hollow hemisphere and is R 2 from C. f = m g sin ⁡ θ ...(i) N - m g cos ⁡ θ ...(ii) N × R 2 sin ⁡ α = R R 2 cos ⁡ α f ...(iii) ∴ tan ⁡ θ = sin ⁡ α 2 - cos ⁡ α ⇒ α = 60 o

A uniform thin hemispherical shall is kept at rest and in equilibrium on an inclined plane of angle of inclination θ = 30 o as shown in figure. If the surface of the inclined plane is sufficiently rough to prevent sliding then the angle α made by the plane of hemisphere with inclined plane is:

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