Question

The centre of mass of a system of two bodies of masses $M$ and $m, (M > m)1$ separated by a distance $d$ is

• A. midway between the bodies
• B. closer to the heavier body
• C. closer to the lighter body
• D. at the centre of the heavier body

Answer 1

Answer: (B)

closer to the heavier body

Answer 2

Let $x_1$ and $x_2$ be distances of centre of mass from the two bodies of masses $M$ and $m (M > m)$ respectively.
As $Mx_1 = mx_2 \:\:\:\:\: \therefore \:\: \frac{x_1}{x_2} = \frac{m}{M}$
$\because \:\: M > m$ or $m < M$
$\therefore \:\:\:\: \frac{x_1}{x_2} < 1$ or $x_1 < x_2$
Thus, the centre of mass is closer to the heavier body.