Q. The distance of a planet from the sun is 5 times, the distance between the earth and the sun. the time period of the planet is
A) $6^{3/2}T\ yr$
B) $5^{3/2}T\ yr$
C) $5^{3/1}T\ yr$
D) $5^{1/2}T\ yr$
Explanation
(b) From Kepler’s third law of planetary motion
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T^{2} \propto R^{3}$
$Given,\ \ \ \ {\ R}_{1} = R,\ \ R_{2} = 5R$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \frac{T_{1}^{2}}{T_{2}^{2}} = \frac{R^{3}}{(5R)^{3}}$
$\Longrightarrow \ \ \ \ \ \ \ \ \frac{T_{1}}{T_{2}} = \frac{1}{(5)^{3/2}}\ \ $
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T_{2} = 5^{3/2}T_{1}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ T_{2} = 5^{\frac{3}{2}}T\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \left\lbrack \therefore T_{1} = T \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.