Question

A frustum of a uniform solid cone has base radius R and height H as shown. Radius of top surface is $\frac{R}{2}$. If height of centre of mass of frustum is $\frac{11H}{4n}$ from base, then $n$ will be

Answer 1

Centre of mass of cone is at one fourth height from its base.
$\Rightarrow y_{cm}=\frac{\rho \times \frac{1}{3}\pi (R{)}^2\times 2H\times \frac{2H}{4}-\rho \times \frac{1}{3}\pi \frac{R^2}{4}H\frac{5H}{4}}{\rho \times \left(\frac{1}{3}\pi \right(R{)}^2\times 2H-\frac{1}{3}\pi \frac{R^2}{4}H)}=\frac{11H}{28}\to x=7$