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

  $2\left(\hat{\mathrm{i}}+\hat{\mathrm{j}}\right)$
• B

  $\left(\hat{\mathrm{i}}+\hat{\mathrm{j}}\right)$
• Correct answer
  C

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

  $\frac{4}{3}\left(\hat{\mathrm{i}}+\hat{\mathrm{j}}\right)$

Hence, the correct answer is option: 'C'.