Question

Three identical spheres, each of mass $M$, are placed at the corners of a right angle triangle with mutually perpendicular sides equal to $2m$ (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of centre of mass

• A. $2\left(\hat{i}+\hat{j}\right)$
• B. $\left(\hat{i}+\hat{j}\right)$
• C. $\frac{2}{3}\left(\hat{i}+\hat{j}\right)$
• D. $\frac{4}{3}\left(\hat{i}+\hat{j}\right)$

Answer 1

Answer: (C)

$X_{\text{com}}=\frac{M\times 0+M\times 2+M\times 0}{3M}=\frac{2}{3}$
$y_{\text{com}}=\frac{M\times 0+M+2+M\times 0}{3M}=\frac{2}{3}$
Position vector $=\frac{2}{3}\hat{i}+\frac{2}{3}\hat{j}$