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JIPMER 2019
Exam
JIPMER
Year
2019
Subject
Physics
Chapter
Gravitation

JIPMER 2019 · Physics · Gravitation

A planet of radius R has a time period of revolution T. Find time...

A planet of radius R has a time period of revolution T. Find time period of a planet of radius 9 R ?

Options

  1. A33T3 \sqrt{3} T
  2. B9T9 T
  3. C27T27 T
  4. D93T9 \sqrt{3} T

Correct answer

C. 27T27 T

Step-by-step solution

By Kepler's third law of planetory motion, Given, T1T2=(a1a2)3/2T1=T,a1=R,T2=?,a2=9RTT2=(R9R)3/2,TT2=[(13)2]3/2TT2=127⇒T2=27 T\begin{aligned} \frac{T_1}{T_2} & =\left(\frac{a_1}{a_2}\right)^{3 / 2} \\ T_1 & =T, a_1=R, T_2=?, a_2=9 R \\ \frac{T}{T_2} & =\left(\frac{R}{9 R}\right)^{3 / 2}, \frac{T}{T_2}=\left[\left(\frac{1}{3}\right)^2\right]^{3 / 2} \\ \frac{T}{T_2} & =\frac{1}{27} \Rightarrow T_2=27 \mathrm{~T} \end{aligned}
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