Question

Two conical portions each of height 2R are removed from a cylinder of length 4R and radius R as shown in figure. If density of the material is $\mathrm{\rho ,}$ then moment of inertia of given system about the axis of cylinder is

• A. $\frac{8}{5}\rho \pi R^5$
• B. $\frac{4}{5}\rho \pi R^5$
• C. $\frac{2}{3}\rho \pi R^5$
• D. $\frac{5}{3}\rho \pi R^5$

Answer 1

The correct option is A $\frac{8}{5}\rho \pi R^5$

$I_{cylinder}$=$I_{core}$$\times$2 + $I_{require}$
$\frac{M{R}^2}{2}=\frac{3}{10}M{R}^2\times 2+I_{require}\frac{\left(\rho \pi R^2\right)\times 4\times R^2}{2}=\frac{3}{10}\frac{\rho \pi R^2\times 2R\times R^2}{3}+I_{require}\Rightarrow I_{require}=2\rho \pi R^5-\frac{2}{5}\rho \pi R^5{I}_{require}=\frac{8}{5}\rho \pi R^5$