System of Particles and Rotational Motion - Result Question 1
1. 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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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} $
