Question

Two particles of mass $2kg$ and $4kg$ are approaching towards each other with acceleration $1m/{sec}^2$ and $2m/{sec}^2$ respectively on a smooth horizontal surface. Find the acceleration of centre of mass of the system.

Answer 1

Given,

$m_1=2kg$

$m_2=4kg$

${\overrightarrow{a}}_1=1\hat{i}m/se{c}^2$

${\overrightarrow{a}}_2=-2\hat{i}m/se{c}^2$

The acceleration of centre of mass of the system,

${\overrightarrow{a}}_m=\frac{m_1{\overrightarrow{a}}_1+m_2{\overrightarrow{a}}_2}{m_1+m_2}$

${\overrightarrow{a}}_m=\frac{2\left(1\hat{i}\right)+4(-2\hat{i})}{2+4}$

${\overrightarrow{a}}_m=\frac{2\hat{i}-8\hat{i}}{6}$

${\overrightarrow{a}}_m=-1m/se{c}^2$