Gravitation - Result Question 4

4. The period of revolution of planet A around the Sun is 8 times that of B. The distance of A from the Sun is how many times greater than that of B from the Sun?

[1997]

(a) 2

(b) 3

(c) 4

(d) 5

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Answer:

Correct Answer: 4. (a)

Solution:

  1. (a) Let $T_A$ and $T_B$ be time period of $A$ and $B$ about sun.

$T_A=8 T_B$

$\frac{T_A}{T_B}=8$

According to Kepler’s Law, $T^{2} \propto r^{3}$

$\frac{T_A}{T_B}=\frac{(r_A)^{3}}{(r_B)^{3}} \Rightarrow(\frac{r_A}{r_B})^{3}=8 \quad \Rightarrow \frac{r_A}{r_B}=2$