Centre of Mass Distance from Particle – Rankers Physics
Topic: Center of Mass , Momentum and Collision
Subtopic: Calculation of Center of Mass

Centre of Mass Distance from Particle

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

(2020)

$50\text{ cm}$
$67\text{ cm}$
$80\text{ cm}$
$33\text{ cm}$

Solution:

Use the centre of mass formula $x_{cm} = \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2}$. Substituting $m_1 = 5\text{ kg}$, $x_1 = 0$, $m_2 = 10\text{ kg}$, $x_2 = 100\text{ cm}$, we get $x_{cm} = \frac{10 \times 100}{15} = 66.67\text{ cm} \approx 67\text{ cm}$. Option (b) is correct.

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