A solid sphere of mass $'M'$ and radius $'a'$ is surrounded by a uniform concentric spherical shell of thickness $2a$ and mass $2M$. The gravitational field at distance $'3a'$ from the centre will be :
- $\frac{2GM}{9a^2}$
- $\frac{GM}{3a^2}$
- $\frac{GM}{9a^2}$
- $\frac{2GM}{3a^2}$
The Correct Option is B
Solution and Explanation
$g. 4 \pi r^2$ = (Mass enclosed) 4$\pi$G
$g = \frac{3M4 \pi G}{4 \pi (3a)^2}$
$= \frac{MG}{3a^2}$
Option (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].