First slide

Location of centre on mass for multiple point masses

Question

Three particles, each of mass m are placed at the vertices of a right angled triangle as shown in figure. The position vector of the centre of mass of the system is (O is the origin and $\hat{i}, \hat{j}, \hat{k}$ are unit vectors) [EAMCET 2013]

Easy

A

$\frac{1}{3} (a \hat{i} - b \hat{j})$
B

$\frac{2}{3} (a \hat{i} - b \hat{j})$
C

$\frac{2}{3} (a \hat{i} + b \hat{j})$
D

$\frac{1}{3} (a \hat{i} + b \hat{j})$

Solution

Given, mass = m
Position of centre of mass, $r_{C M} = \frac{m a \hat{i} + m b \hat{j} + m (0) \hat{k}}{3 m}$
$\Rightarrow$ $r_{C M} = \frac{1}{3} (a \hat{i} + b \hat{j})$

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