Question

On a massless rod four masses are fixed as shown in figure. What is the moment of inertia about an axis passing through centre of rod

• A. $\frac{{{l}^{2}}}{2}\left( M+\frac{m}{4} \right)$
• B. $\frac{{{l}^{2}}}{2}\left( \frac{M}{4}+m \right)$
• C. $\frac{{{l}^{2}}}{4}\left[ M+\frac{m}{4} \right]$
• D. $\frac{{{l}^{2}}}{4}\left[ \frac{M}{4}+m \right]$

Answer 1

Answer: (A)

$\frac{{{l}^{2}}}{2}\left( M+\frac{m}{4} \right)$

Answer 2

Moment of inertia of mass M about axis
$=M\times {{\left( \frac{l}{2} \right)}^{2}}$
Moment of inertia of both the masses having mass
$M=2M\times {{\left( \frac{l}{2} \right)}^{2}}=\frac{M{{l}^{2}}}{2}$
Moment of inertia of masses having mass
$m=2\times m{{\left( \frac{l}{4} \right)}^{2}}=\frac{m{{l}^{2}}}{8}$
Therefore, total moment of inertia
$=\frac{M{{l}^{2}}}{2}+\frac{m{{l}^{2}}}{8}$
$=\frac{{{l}^{2}}}{2}\left[ M+\frac{m}{4} \right]$