Question

A solid cylinder of radius R & length 3R is made of a material having density $\rho$. Now two hemispheres each of radius R is removed from two ends of cylinder as shown in figure. Determine the moment of inertia of this object about axis of cylinder

• A. $\frac{11\pi R^5\rho }{18}$
• B. $\frac{26\pi R^5\rho }{}$
• C. $\frac{29\pi R^5\rho }{30}$
• D. $\frac{26\pi R^5\rho }{15}$

Answer 1

The correct option is C $\frac{29\pi R^5\rho }{30}$

Mass of solid completed cylinder,
$M_1=\pi \left(R{)}^2\right(3R)\rho =3\pi R^3\rho$
Mass of each hemisphere, $M_2=\frac{2}{3}\pi R^3\rho$
Moment of inertia of given structure
$I=I_{cylinder}-2I_{hemisphere}$
$I=\frac{M_1{R}^2}{2}-2\times \left[\frac{2}{5}{M}_2{R}^2\right]=\frac{29}{30}\pi R^5\rho$