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Q.

Two solid spherical planets of equal radii $R$ having masses $4 M$ and $9 M$ their centre are separated by a distance $6 R$ . A projectile of mass $m$ is sent from the planet of mass $4 M$ towards the heavier planet. What is the distance $r$ of the point from the centre of lighter planet where the gravitational force on the projectile is zero ?

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a

$1.4 R$

b

$2.4 R$

c

$1.5 R$

d

$1.8 R$

answer is D.

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Detailed Solution

The gravitational force on projectile of mass $m$ at a distance $r$ from a planet of mass $4 M$ is zero

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$∴ \frac{G (4 M) m}{r^{2}} = \frac{G (9 M) m}{{(6 R - r)}^{2}}$

$\Rightarrow 4 {(6 R - r)}^{2} = 9 r^{2} \Rightarrow 2 (6 R - r) = 3 r ∴ r = 2.4 R$

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Two solid spherical planets of equal radii R having masses 4M and 9M their centre are separated by a distance 6R. A projectile of mass m is sent from the planet of mass 4M towards the heavier planet. What is the distance r of the point from the centre of lighter planet where the gravitational force on the projectile is zero ?