Question

Two objects of same mass $m$ are attached at end of a light rod of length $l$ and rotating about axis $O{O}^{\prime }$ as shown in the figure. The moment inertia of the system about the axis $O{O}^{\prime }$ is

• A. $\frac{m{l}^2}{12}$
• B. $\frac{5m{l}^2}{18}$
• C. $\frac{5m{l}^2}{24}$
• D. $\frac{5m{l}^2}{36}$

Answer 1

The correct option is D $\frac{5m{l}^2}{36}$

As we can see that the mass $m$ in right side is at a $perpendicular$ distance, $r_1=\frac{2l}{3}Sin{30}^0=\frac{l}{3}$ from the axis.

and the mass $m$ in left side is at a $perpendicular$ distance, $r_2=\frac{l}{3}Sin{30}^0=\frac{l}{6}$ from the axis.

and the rod is $massless$ so the MOI of the system will be $I=m{r}_1^2+m{r}_2^2=m\frac{l^2(1+0.25)}{9}=\frac{5m{l}^2}{36}$