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

Question

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

MARKS App · Accepted Answer

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

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