Question

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

• A. $(\frac{2a}{3},\frac{2a}{3})$
• B. $(\frac{4a}{3},\frac{4a}{3})$
• C. $(\frac{a}{3},\frac{a}{3})$
• D. $(\frac{5a}{6},\frac{4a}{9})$

Answer 1

The correct option is A $(\frac{2a}{3},\frac{2a}{3})$

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

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

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

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

so the center of mass of the system will be at $x=\frac{m(0+a+a)}{m+m+m}=\frac{2a}{3}$

and $y=\frac{m(a+0+a)}{m+m+m}=\frac{2a}{3}$

or at $(\frac{2a}{3},\frac{2a}{3})$