The centre of mass of a system of two bodies of masses $M$ and $m,(M>m)$, separated by a distance $d$ is

• A

  midway between the bodies
• Correct answer
  B

  closer to the heavier body
• C

  closer to the lighter body
• D

  at the centre of the heavier body

Solution

The given situation is shown below Let $P$ be the location of centre of mass. If $x_{1}$ and $x_{2}$ be the distances of the centre of mass $P$ from the two bodies of mass $M$ and $m(M>m)$ respectively, then $$ \begin{array}{llrl} & & M x_{1} & =m x_{2} \\ \Rightarrow & & \frac{x_{1}}{x_{2}} & =\frac{m}{M} \\ \text { Since, } & & M>m \\ & \therefore & \frac{x_{1}}{x_{2}} < 1 \\ \Rightarrow & & x_{1} < x_{2} \end{array} $$ Thus, position of centre of mass is closer to the heavier body.

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