Rotational Motion Question 107
Question: In a system of particles 8 kg mass is subjected to a force of 16 N along $+vex-axis$ and another 8 kg mass is subjected to a force of 8 N along $+vey-axis$ . The magnitude of acceleration of centre of mass and the angle made by it with $x-axis$ are given respectively by
Options:
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) $1m{{s}^{-2}},\theta ={{\tan }^{-1}}\sqrt{3}$
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Answer:
Correct Answer: C
Solution:
[c]
$m_1 x_1=m_2 x_2$
$ \vec{a} _{c m}=\frac{\vec{F}}{m}=\frac{16 \hat{i}+8 \hat{j}}{16}=\hat{i}+\frac{1}{2} \hat{j} $
$ \left|\vec{a} _{c m}\right|=\sqrt{1^2+\left(\frac{1}{2}\right)^2}=\frac{\sqrt{5}}{2} \mathrm{~m} / \mathrm{s}^2 $
$ \tan \theta=\frac{1 / 2}{1} \Rightarrow \theta=\tan ^{-1}\left(\frac{1}{2}\right) $
