Q65 / 120 · NEET 2012 (Mains) · Physics

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

  • Correct answer
    A
    $40 \mathrm{~cm}$
  • B
    $45 \mathrm{~cm}$
  • C
    $50 \mathrm{~cm}$
  • D
    $30 \mathrm{~cm}$

Solution

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

Hence, the correct answer is option: 'A'.

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