Question

Three identical spheres each of mass $M$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $3 m$ 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

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