Question

Two bodies of mass $4\, kg$ and $5\, kg$ are moving along east and north directions with velocities $5\, m / s$ and $3\, m / s$ 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, $m_{1}=4\, kg ,\, m_{2}=5\, kg ,\, v _{1}=5 \hat{ j }\, m / s$
$v_{2}=3 \hat{ i } m / s$
$\therefore v _{ CM }=\frac{4 \times 5 \hat{ j }+5 \times 3 \hat{ i }}{5+4}$
$=\frac{20 \hat{ i }}{9}+\frac{15}{9} \hat{ j }$
Hence, magnitude $\left| v _{ CM }\right| =\sqrt{\left(\frac{20}{9}\right)^{2}+\left(\frac{15}{9}\right)^{2}}$
$=\frac{25}{9} m / s$