How will gravitational force change between two bodies when distance between them is halved?

Option 3 : The force would be halved

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10 Questions 10 Marks 10 Mins

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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