A satellite is orbiting just above the surface of the earth with period T. If d is the dependent of the earth and G is the universal constant of gravitation, the quantity 3π/Gd respectively:
A satellite is orbiting just above the surface of the earth with period T. If d is the dependent of the earth and G is the universal constant of gravitation, the quantity 3π/Gd respectively:
T2
T3
\(\sqrt{T}\)
T
The Correct Option is A
Solution and Explanation
The correct option is (A): T2
\(T=\frac{2\pi}{\sqrt{GM}}r^{\frac{3}{2}}\)
\(\Rightarrow T^2=\frac{4\pi^2R^3}{G(\frac{4}{3}\pi R^3d)}(r=R)\)
\(T^2=\frac{3\pi}{Gd}\)
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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].