Question

Two bodies of different masses 4 kg and 8 kg are
moving with speeds 10 m/s and 5 m/s towards each
other. The velocity of centre of mass of the system
is
th
(2) 1 m/s
s
(4) 4 m/s
​

Answer 1

Given :

Two bodies of different masses 4kg and 8kg are moving with speeds 10m/s and 5m/s towards each other.

To Find :

Velocity of centre of mass.

Solution :

❖ Centre of mass is an Imaginary point where the whole mass of system can be assumed to be concentrated.

Velocity of CM of a two particles system is given by

$\dag\:\underline{\boxed{\bf{\purple{\overrightarrow{v}_{CM}=\dfrac{m_1\overrightarrow{v}_1+m_2\overrightarrow{v}_2}{m_1+m_2}}}}}$

By substituting the given values;

$\sf:\implies\:\overrightarrow{v}_{CM}=\dfrac{(4)(8)\hat{i}+(8)(5)(-\hat{i})}{4+8}$

$\sf:\implies\:\overrightarrow{v}_{CM}=\dfrac{32\hat{i}+40(-\hat{i})}{12}$

$\sf:\implies\:\overrightarrow{v}_{CM}=\dfrac{(32-40)\hat{i}}{12}$

$\sf:\implies\:\overrightarrow{v}_{CM}=\dfrac{8(-\hat{i})}{12}$

$:\implies\:\underline{\boxed{\bf{\gray{\overrightarrow{v}_{CM}=0.67(-\hat{i})\:ms^{-1}}}}}$