Question

A man has constructed a toy as shown in figure. If the density of the material of the sphere is $12$ times than of the cone then determine the position of the centre of mass. [Centre of mass of a cone of height h h is at height of $\frac{h}{4}$ from its base.]

Answer 1

$massofthecone=\frac{1}{3}\pi R^{2}H\rho$

$=\frac{1}{3}\pi R^3\rho$

$m_{sphere}=\frac{48}{3}\pi R^3\rho$

$X_{cm}=\frac{m1x2+m2x2}{m1+m2}$

$\frac{4/3p\pi R^3\left(\frac{4R}{4}\right)+\frac{48}{3}\pi R^{3\rho }\left(5R\right)}{4/3\pi R^{3\rho }+\frac{48}{3}\pi R^{3\rho }}$

$X_{cm}=\frac{R+12\left(5R\right)}{1+12}=\frac{61}{R}$