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