Question

A planet of mass m moves round the sun of mass M in a circular orbit of radius r with angular speed omega. Another planet of mass 2m moves round the sun in circular orbit of radius 4rwith angular speed omega'. Find the ratio of omega / omega'.

Answer 1

here gravitational force between planet and sun is balanced by centripetal force.

case 1 : mass of planet = m, mass of sun = M, radius of circular orbit = r and angular speed is $\omega$

then, $\frac{GMm}{r^2}=m\omega^2r$

or, $\omega^2=\frac{GM}{r^3}$......(1)

case 2 : mass of planet = 2m

radius of circular orbit = 4r

and angular speed = $\omega$

then, $\omega'^2=\frac{GM}{(4r)^3}$

or, $\omega'^2=\frac{1}{64}\frac{GM}{r^3}$......(2)

from equations (1) and (2),

$\frac{\omega^2}{\omega'^2}=\frac{64}{1}$

$\frac{\omega}{\omega'}=8$

Answer 2

Answer:

see the attached image

Explanation:

and Mark me as the BRAINLIEST