First slide

Motion of centre of mass

Question

The velocities of two particles A and B of same mass are $\vec{V_{A}} = a \overset{⏞}{i} and \vec{V_{B}} = b \overset{⏞}{j}$ where a and b are constants. The acceleration of particle A is $(2 a \overset{⏞}{i} + 4 b \overset{⏞}{j})$ and acceleration of particle B is $(a \overset{⏞}{i} - b \overset{⏞}{j}) (in m / s^{2})$ . The centre of mass of two particle will move in:

Moderate

A

straight line
B

parabola
C

ellipse
D

circle

Solution

$\vec{V_{com}} = \frac{m_{1} \vec{V_{1}} + m_{2} \vec{V_{2}}}{m_{1} + m_{2}} = \frac{{\vec{V}}_{1} + {\vec{V}}_{2}}{2} = \frac{a \overset{⏞}{i} + b \overset{⏞}{j}}{2}$
$\vec{a_{com}} = \frac{a_{1} + a_{2}}{2} = \frac{3}{2} (a \overset{⏞}{i} + b \overset{⏜}{j})$
${\vec{V}}_{com} is parallel to {\vec{a}}_{com}$ . Hence path will be straight line.

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App