First slide

Methods to locate centre of mass

Question

Three identical spheres, each of mass M, are placed at the corners of a right angle triangle with mutually perpendicular sides equal to 2 m (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the position vector of centre of mass.

Easy

A

$\frac{4}{3} (\hat{i} + \hat{j})$
B

$2 (\hat{i} + \hat{j})$
C

$(\hat{i} + \hat{j})$
D

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

Solution

$\begin{array}{l} x_{cm} = \frac{M \times 0 + M \times 0 + M \times 2}{3 M} = \frac{2}{3} \\ y_{cm} = \frac{M \times 0 + M \times 0 + M \times 2}{3 M} = \frac{2}{3} \\ {\vec{r}}_{cm} = \frac{2}{3} (\hat{i} + \hat{j}) \end{array}$

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