Gravitation - Result Question 5

5. The distance of Neptune and Saturn from the sun is nearly $10^{13}$ and $10^{12}$ meter respectively. Assuming that they move in circular orbits, their periodic times will be in the ratio

(a) 10

(b) 100

(c) $10 \sqrt{10}$

(d) 1000

[1994]

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Answer:

Correct Answer: 5. (c)

Solution:

  1. (c) $T^{2} \propto R^{3}$ (According to Kepler’s law)

$ T_1^{2} \propto(10^{13})^{3} \text{ and } T_2^{2} \propto(10^{12})^{3} $

$\therefore \quad \frac{T_1^{2}}{T_2^{2}}=(10)^{3}$ or $\frac{T_1}{T_2}=10 \sqrt{10}$



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