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A thin hemispherical shell of uniform density and radius $R$ is placed upside down on a rough inclined plane. As the angle of the inclined plane is gradually increased, the shell starts toppling without slipping. Which of the following is true ?

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The angle of inclined plane with horizontal must be $\tan^{- 1} (2)$

Centre of mass of the shell should be vertically above the lowermost point of the shell.

$μ > 2$

$μ < \frac{3}{2}$

answer is A, C.

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Detailed Solution

$m g \sin θ \frac{R}{2} \geq m g \cos θ R$

$\tan θ \geq 2$

$m g \sin θ \leq μ m g \cos θ$

$μ \geq \tan θ$

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