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  4. Three masses are placed on the x-axis: 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70 cm. The distance of the centre of mass from the origin is

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Q. Three masses are placed on the x-axis : $300\, g$ at origin, $500 \,g$ at $x = 40 \,cm$ and $400\, g$ at $x = 70 \,cm$. The distance of the centre of mass from the origin is

AIPMTAIPMT 2012System of Particles and Rotational Motion

Solution:

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The distance of the centre of mass of the system of three masses from the origin $O$ is
$X_{CM}=\frac{m_1 x_1+m_2 x_2+m_3 x_3}{m_1+m_2+m_3}$
$=\frac{300\times0+500\times40+400\times70}{300+500+400}$
$=\frac{500\times40\times400\times70}{1200}=\frac{400[50+70]}{1200}$
$=\frac{50+70}{3}=\frac{120}{3}=40 \,cm$