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 $\mathrm{R}^{-3 / 2}$ then choose the correct option :
(1) $T^{2} \propto R^{5 / 2}$
(2) $\mathrm{T}^{2} \propto \mathrm{R}^{7 / 2}$
(3) $T^{2} \propto R^{3 / 2}$
(4) $T^{2} \propto R^{3}$
Show Answer
Answer: (1)
Solution:
$\mathrm{F}=\frac{\mathrm{GMm}}{\mathrm{R}^{3 / 2}}=\mathrm{m} \omega^{2} \mathrm{R}$
$\omega^{2} \propto \frac{1}{\mathrm{R}^{5 / 2}} \quad \because \mathrm{T}=\frac{2 \pi}{\omega}$ so
$\mathrm{T}^{2} \propto \mathrm{R}^{5 / 2}$
