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How is the gravitational force between two bodies changes if the distance between them triples and mass of both the bodies becomes three times of their original mass-

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Three times

Remains same

One-third

One-ninth

answer is D.

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Detailed Solution

The gravitational force between two bodies remains same if the distance between them triples and mass of both the bodies becomes three times of their original mass.
The force of gravitation between two objects is given by

F = \frac{G m_{1} m_{2}}{r^{2}}

, where

G =

universal gravitation constant,

m_{1} =

mass of first object,

m_{2} =

mass of second object and

r =

distance between them
And when distance between the objects is tripled, i.e.,

r

becomes

3 r

, and the mass of the bodies becoms

3 m_{1}, 3 m_{2}

then the value of force will change as

F^{'} = \frac{G . 3 m_{1} . 3 m_{2}}{{(3 r)}^{2}}

= \frac{1}{9} \frac{9 G m_{1} m_{2}}{r^{2}}

= \frac{G m_{1} m_{2}}{r^{2}}

F^{'} = F

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