The centre of mass of a system of two particles divides. The distance between them is

In inverse ratio of square of masses of particles

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In direct ratio of square of masses of particles

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In inverse ratio of masses of particles

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In direct ratio of masses of particles.

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Solution

The correct option is C In inverse ratio of masses of particles
Let the centre of mass of the system lies at origin.
Using $X_{C M} = \frac{M_{1} X_{1} + M_{2} X_{2}}{M_{1} + M_{2}}$
Or $0 = \frac{M_{1} (- X_{1}) + M_{2} X_{2}}{M_{1} + M_{2}}$
$⟹ M_{1} X_{1} + M_{2} X_{2}$
$⟹ \frac{X_{1}}{X_{2}} = \frac{M_{2}}{M_{1}}$
So, centre of mass divides the distance between the two particles in the inverse ratio of masses of particles.

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The centre of mass of a system of two particles divides. The distance between them is

The correct option is C In inverse ratio of masses of particlesLet the centre of mass of the system lies at origin.Using XCM=M1X1+M2X2M1+M2Or 0=M1(−X1)+M2X2M1+M2⟹ M1X1+M2X2⟹ X1X2=M2M1So, centre of mass divides the distance between the two particles in the inverse ratio of masses of particles.