Three masses are placed on the $x$-axis : $300 \mathrm{~g}$ at origin, $500 \mathrm{~g}$ at $x=40…

Three masses are placed on the $x$-axis : $300 \mathrm{~g}$ at origin, $500 \mathrm{~g}$ at $x=40 \mathrm{~cm}$ and $400 \mathrm{~g}$ at $x=70 \mathrm{~cm}$. The distance of the centre of mass from the origin is
  1. $40 \mathrm{~cm}$
  2. $45 \mathrm{~cm}$
  3. $50 \mathrm{~cm}$
  4. $30 \mathrm{~cm}$

Solution

$\begin{aligned} x_{\mathrm{CM}} & =\frac{m_1 x_1+m_2 x_2+m_3 x_3}{m_1+m_2+m_3} \\ & =\frac{300(0)+500(40)+400(70)}{300+500+400} \\ & =\frac{20000+28000}{1200} \\ & =\frac{48000}{1200} \\ & =40 \mathrm{~cm} \end{aligned}$

Asked in: NEET 2012 (Mains)

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