Question:
A particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius $a$. The magnitude of the gravitational potential at a point situated at $a/2$ distance from the centre, will be :
A particle of mass $M$ is situated at the centre of a spherical shell of same mass and radius $a$. The magnitude of the gravitational potential at a point situated at $a/2$ distance from the centre, will be :
Updated On: May 25, 2022
- $\frac{GM}{a}$
- $\frac{2GM}{a}$
- $\frac{3GM}{a}$
- $\frac{4GM}{a}$
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The Correct Option is C
Solution and Explanation
gravitational potential at $x$ point
$V _{ x }=\frac{ GM }{ a / 2}+\frac{ GM }{ a }=\frac{3\, GM }{ a }$
$V _{ x }=\frac{ GM }{ a / 2}+\frac{ GM }{ a }=\frac{3\, GM }{ a }$
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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].