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
Show Answer
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} $
