Question:
When distance between two bodies is doubled and also mass of each body is doubled, gravitational force between them remains the same.
According to Newton?? law of gravitation, force is directly proportional to product of the mass of bodies and inversely proportional to the square of the distance between them.
When distance between two bodies is doubled and also mass of each body is doubled, gravitational force between them remains the same.
According to Newton?? law of gravitation, force is directly proportional to product of the mass of bodies and inversely proportional to the square of the distance between them.
Updated On: Jul 6, 2022
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The Correct Option is A
Solution and Explanation
According to Newtons law of gravitation, $F = \frac{Gm_{1}m_{2}}{r^{2}}$. When $m_{1}$, $m_{2}$ and $r$ all are doubled, $F= \frac{G\left(2m_{1}\right)\left(2m_{2}\right)}{\left(2r\right)^{2}} = \frac{Gm_{1}m_{2}}{r^{2}}$, i.e. $F$ remains the same.
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Concepts Used:
Gravitation
In mechanics, the universal force of attraction acting between all matter is known as Gravity, also called gravitation, . It is the weakest known force in nature.
Newton’s Law of Gravitation
According to Newton’s law of gravitation, “Every particle in the universe attracts every other particle with a force whose magnitude is,
- F ∝ (M1M2) . . . . (1)
- (F ∝ 1/r2) . . . . (2)
On combining equations (1) and (2) we get,
F ∝ M1M2/r2
F = G × [M1M2]/r2 . . . . (7)
Or, f(r) = GM1M2/r2
The dimension formula of G is [M-1L3T-2].