Question

A rod of length $L$ is composed of a uniform length $\frac{L}{2}$ of wood whose mass in $m_{w}$ and a uniform length $\frac{L}{2}$ of brass whose mass is $m_{b}$. The moment of inertia $I$ of the rod about an axis perpendicular to the rod and through its centre is equal to

• A. $\left(m_{w}+m_{b}\right) \frac{L^{2}}{6}$
• B. $\left(m_{w}+m_{b}\right) \frac{L^{2}}{2}$
• C. $\left(m_{w}+m_{b}\right) \frac{L^{2}}{12}$
• D. $\left(m_{w}+m_{b}\right) \frac{L^{2}}{3}$

Answer 1

Answer: (C)

For a thin uniform rod, moment of inertia about an axis through its centre perpendicular to length of rod, $I=\frac{1}{12} M L^{2}$
Here, $M=\left(m_{w}+m_{b}\right)$
$\therefore I=\frac{1}{12}\left(m_{w}+m_{b}\right) L^{2}$