What happens to the gravitational force between two objects when the distance stays the same but the mass increases?

As the distance between two bodies increases the intensity of gravitational force decreases by a factor of 1/r2, where r = distance between two bodies. The whole business of gravitational force was first put forward by great scientist Sir Isaac Newton. According to his Law of gravitation, the force acting between two bodies is given by F = m1m2/r2 where m1 = mass of object 1 m2 = mass of object 2

Option 3 : The force would be halved

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CONCEPT:

Newton's law of gravitation states that any two bodies having masses (m1 and m2) keeping at a distance (r) from each other exerts a Force of attraction on each other.
- This force is directly proportional to the masses of bodies and inversely proportional to the square of the distance between them.

\(\Rightarrow F \propto \frac{M_1M_2}{R^2} \Rightarrow F = \frac {GM_1M_2}{R^2} \)

Where G = 6.674 × 10-11 m3Kg-1s-2 is a universal constant

The dimension of the force is MLT-2 and the SI unit is Newton (N).

CALCULATION:

Given: Mass of the one body (M1) = M, Mass of the another body (M2) = 2M, initial distance = R, Final distance = 2R,F = Initial Force, F' = Final force

M1 = M, M2 = 2M, R' = 2R

\(\Rightarrow F \propto \frac{M_1M_2}{R^2}\)

\(F'=\frac{GM_1M_2}{R'^2} =\frac{G M_1(2M_2)}{(2R)^2}=\frac {2GM_1M_2}{4R^2}=\frac {1}{2}F\)

Hence, the Force would be halved is the correct answer.

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