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Gravitation question

2015 · Q145
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Gravitation question

2015 · Q145

NEETPhysicsGravitationMCQ+4 / −1
Kepler's third law states that square of period of revoluation (T) of a planet around the sun, is proportional to third power of average distance r between sun and planet i.e. T2 = Kr3 here K is constant. If the masses of sun and planet are M and m respectively then as per Newton's law of gravitation force of attraction between them is F = GMmr2{{GMm} \over {{r^2}}}r2GMm​, here G is gravitational constant. The relation between G and K is described as
  1. A
    K = G
  2. B
    K = 1G{1 \over G}G1​
  3. C
    GK = 4π\piπ2
  4. D
    GMK = 4π\piπ2
View written solutionFree

Correct answer: D

Gravitational force of attraction between planet and sun gives centripetal force,

GMm/r2 = mv2/r

Now velocity v = GM/r\sqrt {GM/r} GM/r​

Time period of planet T = 2π\pi πr/v
⇒\Rightarrow⇒ T2 = 4π2\pi ^2π2r3/GM

From Kepler’s third law, T2 = Kr3

Using equations, we see 4π\piπ2r3/GM = Kr3,

so relation between G and K is GMK = 4π2\pi ^2π2

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