First slide

Methods to locate centre of mass

Question

Three identical spheres each of radius R are placed touching each other on a horizontal table as shown in figure. The co-ordinates of centre of mass are:

Moderate

A

(R, R)
B

(0, 0)
C

( $\frac{R}{2}, \frac{R}{2}$ )
D

$(R, \frac{R}{\sqrt{3}})$

Solution

$x_{cm} = \frac{m \times 0 + m \times 2 R + mR}{3 m} = R$
$y_{cm} = \frac{m \times 0 + m \times 0 + mR \sqrt{3}}{3 m} = \frac{R}{\sqrt{3}}$

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