Question

Four point masses, each of value m, are placed at the corners of a square ABCD of side $\iota$ The moment of inertia through A and parallel to BD is :

• A. $m{l}^2$
• B. $2m{l}^2$
• C. $\sqrt{3}m{l}^2$
• D. $3m{l}^2$

Answer 1

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

$bysymmetry{r}_1=r_2{r}_1=\frac{l}{\sqrt{2}}=2r{r}_3=\sqrt{2}lMOI=\sum m_i{r}_i^2=m(\frac{l}{\sqrt{2}}{)}^2+m(\sqrt{2}l{)}^2+m(\frac{l}{\sqrt{2}}{)}^2=3m{l}^2$