Question

Three identical spheres, each of mass $M$, are placed at the corners of a right angle triangle with mutually perpendicular sides equal to $2\,m$ (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)

$\frac{2}{3}\left(\hat{i}+\hat{j}\right)$

Answer 2

$X_{\text{com}}=\frac{M\times0+M\times2+M\times0}{3M}=\frac{2}{3}$ $y_{\text{com}}=\frac{M\times0+M+2+M\times0}{3M}=\frac{2}{3}$ Position vector $=\frac{2}{3} \hat{i}+\frac{2}{3} \hat{j}$