The distance of two planets from the sun are 10¹³ m and 10¹² m respectively. The ratio of time periods of the planets is (a) √(10) (b) 10√(10) (c) 10 (d) (1)/(√(10))

Answer: (b). Kepler's third law: T ∝ r3/2. (T₁)/(T₂) = (10¹³10¹²)3/2 = 103/2 = 10√(10) So the answer is (b) 10√(10).

The distance of two planets from the sun are 10¹³ m and 10¹² m… | NEET 1988 (AIPMT)

Q33NEET 1988 · AIPMTEasy

Kepler's Laws & Planetary Motion

The distance of two planets from the sun are $10^{13}\text{ m}$ and $10^{12}\text{ m}$ respectively. The ratio of time periods of the planets is

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Answer: (b)

Kepler's third law: $T \propto r^{3/2}$ .
$\dfrac{T_1}{T_2} = \left(\dfrac{10^{13}}{10^{12}}\right)^{3/2} = 10^{3/2} = 10\sqrt{10}$
So the answer is (b) $10\sqrt{10}$ .