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Sand is to be piled up on a horizontal ground in the form of a regular cone of a fixed base of radius R. Coefficient of static friction between the sand layers is $μ$ . Maximum volume of the sand that can be piled up in the form of cone without slipping on the ground is

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$\frac{μ R^{3}}{3 π}$

$\frac{μ R^{3}}{3}$

$\frac{π R^{3}}{3 μ}$

$\frac{μ π R^{3}}{3}$

answer is D.

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Detailed Solution

$μ = Tan θ = \frac{h}{R} v = \frac{1}{3} π R^{2} h$

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