Question:
Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1m, 2m, 4m, 8m, ...., respectively, from the origin. The resulting gravitational potential due to this system at the origin will be
Infinite number of bodies, each of mass 2 kg are situated on x-axis at distance 1m, 2m, 4m, 8m, ...., respectively, from the origin. The resulting gravitational potential due to this system at the origin will be
Updated On: May 25, 2022
- $ - 4 G $
- $ - G$
- $- \frac{8}{3} G$
- $ - \frac{4}{3} G$
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The Correct Option is A
Solution and Explanation
$V = - G (2)\bigg[\frac{1}{1} +\frac{1}{2}+ \frac{1}{4} + \frac{1}{8}+...........\bigg] $
$= - 2G\bigg[ \frac{1}{1 - 1/2}\bigg] = - 4G $
$= - 2G\bigg[ \frac{1}{1 - 1/2}\bigg] = - 4G $
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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].