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Standard XII

Physics

Newton's Law of Gravitation

Two particles...

Question

Two particles of mass M and 2M are at distance D apart. under their mutual force they start moving towards each other. the acceleration of their center of mass when they are D/2 apart is

2 G M / D^{2}

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4 G M / D^{2}

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8 G M / D^{2}

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0

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Solution

The correct option is D $0$
$F = (G \times 2 m \times m) / (d \times d)$
acceleration of mass $m = G \times 2 m / d \times d$
acceleration of mass $2 m = - G \times m / d \times d$
so acceleration of centre of mass $= (m \times G \times 2 m / d \times d - m \times G \times 2 m / d \times d) / (2 m + m)$
$= 0$

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Two particles of mass M and 2M are at distance D apart. under their mutual force they start moving towards each other. the acceleration of their center of mass when they are D/2 apart is

The correct option is D 0F=(G×2m×m)/(d×d)acceleration of mass m=G×2m/d×dacceleration of mass 2m=−G×m/d×dso acceleration of centre of mass=(m×G×2m/d×d−m×G×2m/d×d)/(2m+m)=0