Gravitation Question 2
Question 2 - 2024 (01 Feb Shift 2)
A light planet is revolving around a massive star in a circular orbit of radius $R$ with a period of revolution $T$. If the force of attraction between planet and star is proportional to $R^{-3 / 2}$ then choose the correct option :
(1) $T^{2} \propto R^{5 / 2}$
(2) $T^{2} \propto R^{7 / 2}$
(3) $T^{2} \propto R^{3 / 2}$
(4) $T^{2} \propto R^{3}$
Show Answer
Answer: (1)
Solution:
$F=\frac{GMm}{R^{3 / 2}}=m \omega^{2} R$
$\omega^{2} \propto \frac{1}{R^{5 / 2}} \quad \because T=\frac{2 \pi}{\omega}$ so
$T^{2} \propto R^{5 / 2}$
