System Of Particles And Rotational Motion Ques 8
8. Two particles of mass $5 $ $kg$ and $10$ $ kg$ respectively are attached to the two ends of a rigid rod of length $1 $ $m$ with negligible mass. The centre of mass of the system from the $5$ $kg$ particle is nearly at a distance of :
[2020]
(a) $50 $ $cm$
(b) $67 $ $cm$
(c) $80 $ $cm$
(d) $33 $ $cm$
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Answer:
Correct Answer: 8.(b)
Solution:
- (b)
Centre of mass of a system of two particles of masses $m_1$ and $m_2$ having position vectors $\overrightarrow{{}x_1}$ and $\overrightarrow{{}x_2}$ is
$ x _{cm}=\frac{m_1 x_1+m_2 x_2}{m_1+m_2} $
Taking particle of mass $5 $ $kg$ at origin.
$ \begin{aligned} & \Rightarrow x _{cm}=\frac{5 \times 0+100 \times 10}{5+10}=\frac{200}{3}=66.66 cm \\ & \Rightarrow x _{cm}=67 cm \end{aligned} $
BETA
