The time period of a satellite revolving around earth in a given orbit is 7 hours. If the radius of orbit is increased to three times its previous value, then approximate new time period of the satellite will be
- 40 hours
- 36 hours
- 30 hours
- 25 hours
The Correct Option is B
Solution and Explanation
The correct answer is (B) : 36 hours
\(T_{2}^2 = ( \frac{R_2}{R_1} )^3 T^2{_1}\)
\(⇒ T_2 = (3)^{3/2} × 7 ≈ 5.2 × 7\)
T2 ≅ 36 hrs
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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].