Question

Three rods of the same mass are placed as shown in the figure. What will be the co-ordinate of centre of mass of the system?

Answer 1

for a rod its center of mass is $mid$ point of this rod.

So the CM of vertical rod will be $(0,\frac{a}{2})$

the CM of horizontal rod will be $(\frac{a}{2},0)$

the CM of inclined rod will be $(\frac{a}{2},\frac{a}{2})$

so the center of mass of the system will be at $x=\frac{m(0+0.5a+0.5a)}{m+m+m}=\frac{a}{3}$

and $y=\frac{m(0.5a+0+0.5a)}{m+m+m}=\frac{a}{3}$

or at $(\frac{a}{3},\frac{a}{3})$