Question

The coordinate of the centre of mass of a system as shown in figure :-

• A. $(\frac{a}{3},0)$
• B. $(\frac{a}{2},\frac{a}{2})$
• C. $(\frac{a}{3},\frac{a}{3})$
• D. $(0,\frac{a}{3})$

Answer 1

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

We know,

$X_{c.o.m}=\frac{\Sigma m_i{x}_i}{\Sigma m_i}$

$\Rightarrow X_{c.o.m}=\frac{M\left(0\right)+M\left(0\right)+M\left(a\right)}{3M}$

$\Rightarrow X_{c.o.m}=\frac{a}{3}$

Similarily,

$Y_{c.o.m}=\frac{\Sigma m_i{y}_i}{\Sigma m_i}$

$\Rightarrow Y_{c.o.m}=\frac{M\left(a\right)+M\left(0\right)+M\left(0\right)}{3M}$

$\Rightarrow Y_{c.o.m}=\frac{a}{3}$

Therefore, C is correct option.