Laws Of Motion Question 409

Question: A worker piles up sand onto a circular area of radius R. No sand is to spill onto the surrounding area. The coefficient of friction of sand on sand is $ \mu $ . The greatest volume of the sand that can be stored in the manner is

Options:

A) $ \frac{\pi \mu R^{3}}{3} $

B) $ \frac{\pi \mu R^{3}}{6} $

C) $ \frac{\pi R^{3}}{3\mu } $

D) None

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Answer:

Correct Answer: A

Solution:

The weight component of a particle is balanced by static friction

$ mg\sin \theta =\mu (mg\cos \theta ) $

$ \mu =\tan \theta =\frac{h}{R} $

So $ h=\mu R $

Volume $ =\frac{1}{3}\pi R^{2}h=\frac{1}{3}\pi R^{2}(\mu R)=\frac{\pi \mu R^{3}}{3} $



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