Question

Two friends Prakash and Naveen are trying to build castles on a seashore in the form of a conical pile of sand. For this they are provided with the following data:
$1)$ Volume of sand $=225c{m}^3$
$2)$ Co-efficient of friction between sand grains, ${\mu }_S=\sqrt{1.6}$
With the recently acquired knowledge about the friction, they realize that for a given amount of sand, they are able to build the pile only till certain maximum height $h$ . Find the approximate maximum height $h$ (in $cm$ ).

Answer 1

Answer: 7

For sand net to fall $tan\theta ={\mu }_s$
$\frac{h}{r}={\mu }_s$
$V=\frac{1}{3}\pi r^{2}h$
$225=\frac{1}{3}\times \pi \times \frac{h^2}{{\mu }_s^2}\times h$
$h^3=\frac{225\times 3\times {\mu }_s^2}{\pi }$
$h^3=\frac{225\times 3\times 1.6}{22}\times 7$
$h^3\approx 343$
$h=7cm$