Separation between earth and sun is given by 1.5 × 106 km. Time period of another planet is 2.83 year. Find distance of another planet from sun?
Separation between earth and sun is given by 1.5 × 106 km. Time period of another planet is 2.83 year. Find distance of another planet from sun?
3 × 106 km
2 × 107 km
3 × 107 km
2 × 106 km
The Correct Option is A
Solution and Explanation
T2 ∝ R3
(T1/T2)2 = (R1/R2)3
\((\frac{1}{2.83})^2\) = {(1.5 x 106)/R2}3
R2 = \((1.5 × 10^{6}) (2.83)\frac{2}{3}\) km
= \((1.5 × 10^{6}) (8)\frac{1}{3}\)
= 3 × 106 km
The correct option is (A): 3 × 106 km
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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].