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:
- (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, $T^{2} \propto r^{3}$
$\frac{T_A}{T_B}=\frac{(r_A)^{3}}{(r_B)^{3}} \Rightarrow(\frac{r_A}{r_B})^{3}=8 \quad \Rightarrow \frac{r_A}{r_B}=2$
