Question

Two bodies of mass $4kg$ and $5kg$ are moving along east and north directions with velocities $5m/s$ and $3m/s$ respectively. Magnitude of the velocity of centre of mass of the system is

• A. $\frac{25}{9}m/s$
• B. $\frac{9}{25}m/s$
• C. $\frac{41}{9}m/s$
• D. $\frac{16}{9}m/s$

Answer 1

Answer: (A)

Velocity of centre of mass is
$v_{CM}=\frac{m_1{v}_1+m_2{v}_2}{m_1+m_2}$
Given, $m_1=4kg,m_2=5kg,v_1=5\hat{j}m/s$
$v_2=3\hat{i}m/s$
$\therefore v_{CM}=\frac{4\times 5\hat{j}+5\times 3\hat{i}}{5+4}$
$=\frac{20\hat{i}}{9}+\frac{15}{9}\hat{j}$
Hence, magnitude $\left|v_{CM}\right|=\sqrt{{\left(\frac{20}{9}\right)}^2+{\left(\frac{15}{9}\right)}^2}$
$=\frac{25}{9}m/s$