Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  JEEMAIN and AIPMT  >>  Physics  >>  Class11  >>  Gravitation
0 votes

What is the radius of moon's orbit around earth assuming the orbit to be circular ($g=9.8 m/s^2$; Radius of earth =6400 km; period of rotation of moon around the earth $=27.3\; days$

\[(a)\;6400\;km \quad (b)\;3.8 \times 10^8\;m \quad (c)\;1000\;km \quad (d)\;10000\;km\]
Can you answer this question?

1 Answer

0 votes
Let orbital radius of moon be $R_0$ and radius of earth be R. mass of earth M mass of moon m, orbital velocity of moon v and its orbital time period be T
For moon resolving around earth
Gravitational force =centrepetal force
$\large\frac{gR^2}{R_0}$$=v^2 =\bigg(\large\frac{2 \pi R_0}{T}\bigg)^2$
$\qquad= \large\frac{4 \pi^2 {R_0}^2}{T^2}$
${R_0}^3=\large\frac{gR^2T^2}{4 \pi ^2}$
$R_0=\bigg[\large\frac{g \pi ^2 T^2}{4 \pi ^2}\bigg]^{\large\frac{1}{3}}$
$R_0=\bigg[\large\frac{9.8 (6.4 \times 10^6)^2 (27.3 \times 86400)^2 }{4(3.14)^2}\bigg]^{\Large\frac{1}{3}}$
$\qquad= 3.83 \times 10^8 \;m$
Hence b is the correct answer.


answered Aug 20, 2013 by meena.p
edited Feb 17, 2014 by meena.p

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App