Question

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

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

Answer 1

Answer: (B)

$(5m,4m,7m)$

particle $-1$
$t=0$ $x=2m$ at $t=1$ $x=x+2v$

$y=4m$ $\Rightarrow x=2+2=4m$

$z=6m$ $y=y=4m$

$z=z=6m$

particle $-2$

$t=o$ at $t=1\sec$

$x_1=6m$ $x_1^1=x_1+0=6m$

$y_1=2m$ $y_1^1=y_1+2x_1=4m$

$z_1=8m$ $z_1^1=z_1+0=8m$

center of mass $x_{c.m}=\frac{m_1{x}^1+m_2{x}_1^1}{m_1+m_2}=\frac{m}{2m}(4+6)$

$\Rightarrow x_{c.m}=5$ meter

$y_{c.m}=\frac{m_1{y}^1+m_2{y}_1^1}{m_1+m_2}=\frac{m}{2m}(4+4)=4$ meter

$z_{c.m}=\frac{m_1{z}^1+m_2{z}_1^1}{m_1+m_2}=\frac{m}{2m}(6+8)=7$ meter

$\Rightarrow$ coordinates $(5m,4m,7m)$