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
The centre of mass of a system of two bodies of masses $M$ and $m, (M > m)1$ separated by a distance $d$ is
Updated On: May 12, 2024
- midway between the bodies
- closer to the heavier body
- closer to the lighter body
- at the centre of the heavier body
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The Correct Option is B
Solution and Explanation
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.
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.
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