The radii of the circular orbits of two satellites around earth are in the ratio $1:4.$ The ratio of their periods of revolution is :

 

One satellite of mass $\mathrm{m}$ is at a distance $\mathrm{r}$ from earth's centre and the other of mass $2\mathrm{m}$ is at a distance $2 \mathrm{r}$ from earth's centre. Their time-period are in the ratio :

Imagine a light planet revolving around a very massive star in a circular orbit of radius $\mathrm{R}$ with a period of revolution $\mathrm{T}.$ If the gravitational  force of attraction between the planet and the star is proportional to ${\mathrm{R}}^{-5/2}, \mathrm{then} :$

A geostationary satellite revolves around the earth in a circular orbit of radius $3600\mathrm{km}.$ Then, spy satellite revolving in a circular orbit a few hundred $\mathrm{km}$ height from the surface of the earth, has the time-period nearly :

A synchronous relay satellite reflects T.V. signals and transmits T.V. programs from one part of the world to the other because its:

The mean radius of earth is ${\mathrm{R}}_{\mathrm{e}},$ its axial angular speed is $\mathrm{\omega }$ and acceleration due to gravity at its surface is $\mathrm{g}.$ The cube of the radius of the orbit of geostationary satellite is:

Orbital radius of a satellite $\mathrm{S}$ of earth is four times the orbital radius of a telecom satellite. The period of revolution of $\mathrm{S}$ IS:

Two spherical planets $\mathrm{P} \mathrm{and} \mathrm{Q}$ have the same uniform density $\mathrm{\rho },$ masses ${\mathrm{M}}_{\mathrm{P}} \mathrm{and} {\mathrm{M}}_{\mathrm{Q}},$ and surface areas $\mathrm{A} \mathrm{and} 4\mathrm{A},$ respectively. A spherical planet $\mathrm{R}$ also has uniform density $\mathrm{\rho }$ and its mass is $\left({\mathrm{M}}_{\mathrm{P}} \mathrm{and} {\mathrm{M}}_{\mathrm{Q}}\right).$ The escape velocities from the planets $\mathrm{P},\mathrm{Q} \mathrm{and} \mathrm{R} \mathrm{are} {\mathrm{v}}_{\mathrm{P}}, {\mathrm{v}}_{\mathrm{Q}} \mathrm{and} {\mathrm{v}}_{\mathrm{R}}$ respectively. Then 

Four particles, each of mass $\mathrm{M}$ and equidistant from each other, move along a circle of radius $\mathrm{R}$ under the action of their mutual gravitational attraction. The speed of each particles is :