Question:
A point mass $m$ is placed inside a spherical shell of radius $R$ and mass $M$ at a distance $\frac{R}{2}$ from the centre of the shell. The gravitational force exerted by the shell on the point mass is
A point mass $m$ is placed inside a spherical shell of radius $R$ and mass $M$ at a distance $\frac{R}{2}$ from the centre of the shell. The gravitational force exerted by the shell on the point mass is
Updated On: Jul 5, 2022
- $\frac{GMm}{R^{2}}$
- $\frac{2GMm}{R^{2}}$
- zero
- $\frac{4GMm}{R^{2}}$
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The Correct Option is C
Solution and Explanation
If a point mass is placed inside a uniform spherical shell, the gravitational force on the point mass is zero. Hence, the gravitational force exerted by the shell on the point mass is zero.
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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].