Question

Two particles of equal mass have coordinates $(2\text{m},4\text{m},6\text{m})$ and $(6\text{m},2\text{m},8\text{m})$. Of these one particle has a velocity $\overrightarrow{v_1}=\left(2\hat{i}\right)\text{m/s}$ and another particle has velocity $\overrightarrow{v_2}=\left(2\hat{j}\right)\text{m/s}$ at time $t=0$. The coordinate of their centre of mass at time $t=1\text{s}$ will be

• A. $(4\text{m},4\text{m},7\text{m})$
• B. $(5\text{m},4\text{m},7\text{m})$
• C. $(2\text{m},4\text{m},6\text{m})$
• D. $(4\text{m},5\text{m},4\text{m})$

Answer 1

The correct option is B $(5\text{m},4\text{m},7\text{m})$

After $1s$, coordinates of first particle will become $(4\text{m},4\text{m},6\text{m})$and co-ordinates of second particle will become $(6\text{m},4\text{m},8\text{m})$.
$\therefore X_{CM}=\frac{4+6}{2}=5\text{m}$
$Y_{CM}=\frac{4+4}{2}=4\text{m}$
and $Z_{CM}=\frac{6+8}{2}=7\text{m}$
Note in this problem answer is independent of the fact whether the first particle has velocity $\overrightarrow{v_1}$ or $\overrightarrow{v_2}$.