question_answer

In a system of particles 8 kg mass is subjected to a force of 16 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

A) \[\frac{\sqrt{5}}{2}m{{s}^{-2}},\theta ={{45}^{0}}\]

B) \[3\sqrt{5}\,m{{s}^{-2}},\theta ={{\tan }^{-1}}(2/3)\]

C) \[\frac{\sqrt{5}}{2}\,m{{s}^{-2}},\theta ={{\tan }^{-1}}(1/2)\]

D) \[1\,m{{s}^{-2}},\theta ={{\tan }^{-1}}\sqrt{3}\]

Correct Answer: C

Solution :

[c] \[{{m}_{1}}{{x}_{1}}={{m}_{2}}{{x}_{2}}\], \[{{\vec{a}}_{cm}}=\frac{{\vec{F}}}{m}=\frac{16\hat{i}+8\hat{j}}{16}=\hat{i}+\frac{1}{2}\hat{j}\] \[\left| {{{\vec{a}}}_{cm}} \right|=\sqrt{{{1}^{2}}+{{\left( \frac{1}{2} \right)}^{2}}}=\frac{\sqrt{5}}{2}m/{{s}^{2}}\] \[\tan \theta =\frac{1/2}{1}\Rightarrow \theta ={{\tan }^{-1}}\left( \frac{1}{2} \right)\]