Question

Three identical spheres each of mass $M$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $3m$ each. Taking point of intersection of mutually perpendicular sides as origin, the magnitude of position vector of centre of mass of the system will be $\sqrt{x}m$. The value of $x$ is

Answer 1

Answer: 2

${\vec{r}}_{com}=\frac{M(0\hat{i}+0\hat{j})+M(3\hat{i})+M(3\hat{j})}{3M}$
${\vec{r}}_{com}=\hat{i}+\hat{j}$
$\left|{\vec{r}}_{com}\right|=\sqrt{2}=\sqrt{x}$
$x=2$