Question:
Two equal masses separated by a distance d attract each other with a force (F). If one unit of mass is transferred from one of them to the Other, the force
Two equal masses separated by a distance d attract each other with a force (F). If one unit of mass is transferred from one of them to the Other, the force
Updated On: Jun 21, 2022
- does not change
- decreases by $(G/d^2)$
- becomes $d^2$ times
- increases by $(2G/d^2)$
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The Correct Option is B
Solution and Explanation
$
F _{(\text {initial) }}=\frac{\text { G.m.m }}{ d ^{2}} \\
F _{(\text {final })}=\frac{\text { G. }( m +1) \cdot( m -1)}{ d ^{2}}=\frac{ G \cdot\left( m ^{2}-1\right)}{ d ^{2}}$
Clearly from above expressions we have a decrease in force by $\frac{ G }{ d ^{2}}$.
F _{(\text {initial) }}=\frac{\text { G.m.m }}{ d ^{2}} \\
F _{(\text {final })}=\frac{\text { G. }( m +1) \cdot( m -1)}{ d ^{2}}=\frac{ G \cdot\left( m ^{2}-1\right)}{ d ^{2}}$
Clearly from above expressions we have a decrease in force by $\frac{ G }{ d ^{2}}$.
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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].