Q.
Two spheres each of mass $M$ and radius $R/2$ are connected with a massless rod of length $2R$ as shown in the figure. What will $b$ be the moment of inertia of the system about an axis passing through the centre of one of the sphere and perpendicular to the rod
A) $\frac{21}{5}MR^{2}$
B) $\frac{2}{5}MR^{2}$
C) $\frac{5}{2}MR^{2}$
D) $\frac{5}{21}MR^{2}$
Explanation
(a) [image:7_image98.emf]
Moment of inertia of the system about $yy^{''}$
$I_{yy^{''}} =$Moment of inertia of sphere $P$ about
$yy^{''} +$ Moment of inertia of sphere $Q$ about $yy^{''}$
Moment of inertia of sphere $P$ about $yy^{''}$
$= \frac{2}{5}\ M\left( \frac{R}{2} \right)^{2} + M(x)^{2}$
$= \frac{2}{5}M\ \left( \frac{R}{2} \right)^{2} + M(2R)^{2}$
$= \frac{MR^{2}}{10} + 4MR^{2}$
Moment of inertia of sphere $Q$ about $yy^{''}$ is $\frac{2}{5}M\left( \frac{R}{2} \right)^{2}$
Now, $I_{yy^{''}} = \frac{MR^{2}}{10} + 4MR^{2} + \frac{2}{5}M\left( \frac{R}{2} \right)^{2} = \frac{21}{5}MR^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.