Question

$\begin{array}{c}\text{There are four point masses meach on the comers of}\\ \text{a square of side length. What is the moment of inertia}\\ \text{of the system about one of its diagonals:}\end{array}$

• A. $2{ml}^2$
• B. $3m{l}^2$
• C. $4m{l}^2$
• D. $6m^2$

Answer 1

The correct option is B $3m{l}^2$

$\because AO\cos {45}^0=\frac{l}{2}$

$\therefore AO\times \frac{1}{\sqrt{2}}=\frac{l}{2}$

$or,AO=\frac{l}{\sqrt{2}}$

$I=I_D+I_B+I_C$

$or,I=\frac{2m{l}^2}{2}+m{\left(\frac{2l}{\sqrt{2}}\right)}^2$

$I=\frac{2m{l}^2}{2}+\frac{4m{l}^2}{2}$

$or,I=\frac{6m{l}^2}{2}=3m{l}^2$

Hence,

option $\left(B\right)$ is correct answer.