Two spheres of masses $16 k g$ and $4 k g$ are separated by a distance $30 m$ on a table. Then the distance from sphere of mass $16 k g$ at which the net gravitational force becomes zero is:

10 m

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20 m

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15 m

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5 m

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Solution

The correct option is B $20 m$
Gravitational force on a mass $m$ at a distance $x$ from $16 k g$ mass is $\frac{16 G m}{x^{2}}$ .
Gravitational force on the mass due to $4 k g$ in the opposite direction is $\frac{4 G m}{(30 - x)^{2}}$
For net force to be zero on the mass,
$\frac{16 G m}{x^{2}} = \frac{4 G m}{(30 - x)^{2}}$
$⟹ x = 20 m$

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Two spheres of masses 16 kg and 4 kg are separated by a distance 30 m on a table. Then the distance from sphere of mass 16 kg at which the net gravitational force becomes zero is:

The correct option is B 20 mGravitational force on a mass m at a distance x from 16 kg mass is 16Gmx2.Gravitational force on the mass due to 4kg in the opposite direction is 4Gm(30−x)2For net force to be zero on the mass,16Gmx2=4Gm(30−x)2⟹x=20 m

Two spheres of masses $16 k g$ and $4 k g$ are separated by a distance $30 m$ on a table. Then the distance from sphere of mass $16 k g$ at which the net gravitational force becomes zero is: