First slide

Motion of centre of mass

Question

In a system of particles 8 kg mass is subjected to a force of l6 N along +ve x-axis and another 8 kg mass is subjected to a force of 8 N along +ve y-axis. The magnitude of acceleration of centre of mass and the angle made by it with x-axis are given respectively by:

Moderate

A

$\frac{\sqrt{5}}{2} {ms}^{- 2}, θ = 45 °$
B

$3 \sqrt{5} {ms}^{- 2}, θ = \tan^{- 1} (\frac{2}{3})$
C

$\frac{\sqrt{5}}{2} {ms}^{- 2}, θ = \tan^{- 1} (\frac{1}{2})$
D

3 $1 {ms}^{- 2}, θ = \tan^{- 1} \sqrt{3}$

Solution

$m_{1} x_{1} = m_{2} x_{2},$
${\vec{a}}_{cm} = \frac{\vec{F}}{m} = \frac{16 \hat{i} + 8 \hat{j}}{16} = \hat{i} + \frac{1}{2} \hat{j}$
$| {\vec{a}}_{cm} | = \sqrt{1^{2} + {(\frac{1}{2})}^{2}} = \frac{\sqrt{5}}{2} m / s^{2}$
tan $θ = \frac{\frac{1}{2}}{1} \Rightarrow θ = \tan^{- 1} (\frac{1}{2})$

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