SATHEE: System of Particles and Rotational Motion

System of Particles and Rotational Motion - Result Question 1

1. Two particles of mass $5 k g$ and $10 k g$ 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 $k g$ particle is nearly at a distance of : [2020]

(a) $50 c m$

(b) $67 c m$

(d) $33 c m$

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Solution:

Centre of mass of a system of two particles of masses $m_{1}$ and $m_{2}$ having position vectors $\vec{x_{1}}$ and $\vec{x_{2}}$ is

$x_{c m} = \frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}$

Taking particle of mass $5 k g$ at origin.

$\begin{aligned} \Rightarrow x_{c m} = \frac{5 \times 0 + 100 \times 10}{5 + 10} = \frac{200}{3} = 66.66 c m \\ \Rightarrow x_{c m} = 67 c m \end{aligned}$

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System of Particles and Rotational Motion - Result Question 1

1. Two particles of mass 5kg and 10kg respectively are attached to the two ends of a rigid rod of length 1m with negligible mass. The centre of mass of the system from the 5 kg particle is nearly at a distance of : [2020]

Solution:

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1. Two particles of mass $5 k g$ and $10 k g$ 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 $k g$ particle is nearly at a distance of : [2020]