Question

The distance of centres of mass of two squre plates system as shown from point O. If masses of plates are 2m and m is (their edges are 'a' and '2a',respectively).Find the distance of centre of mass of the system from O.

• A. $\frac{a}{2}$
• B. $a$
• C. $\frac{3a}{2}$
• D. $\frac{2a}{3}$

Answer 1

The correct option is B $a$

$\begin{array}{c}{x}_{com}=\frac{2m\left(a/2\right)+m\left(2a\right)}{3m}\\ =\frac{3a+2ma}{3m}=\frac{3ma}{3m}=a\\ y_{com}=\frac{2m\left(a/2\right)+m\left(-a\right)}{3m}=0\\ \therefore dis\tan ce=\sqrt{{\left(x_{com}\right)}^2+{\left(y_{com}\right)}^2}\\ =\sqrt{{\left(a\right)}^2+{\left(0\right)}^2}=\sqrt{a^2}=a\end{array}$

Hence,

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