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:
- (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 $\frac{T_1}{T_2}=10 \sqrt{10}$
