G L Mittal and TARUN MITTAL Solutions for Chapter: Gravitation : Planets and Satellites, Exercise 2: NUMERICALS

How much energy would be needed for a $100\mathrm{kg}$ body to escape from the earth? $(\mathrm{g}=10{\mathrm{ms}}^{-2}$ and radius of the earth $R_e=6.4\times {10}^6\mathrm{m})$

If the radius of the earth be $6.38\times {10}^6\mathrm{m}$ and the acceleration due to gravity at earth be $9.8{\mathrm{ms}}^{-2},$ then calculate the escape velocity of a body from the earth's surface.

Mass of the moon is $7.34\times {10}^{22}\mathrm{kg}$ and mean radius $1.74\times {10}^6\mathrm{m}.$ If $\mathrm{G}=6.67\times {10}^{-11}{\mathrm{Nm}}^2{\mathrm{kg}}^{-2},$ then calculate the escape velocity on the moon's surface.

The radius of planet is four times that of the moon. The acceleration due to gravity $\left({\mathrm{g}}_{\mathrm{m}}\right)$ on the moon is $\raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$5,$}\right.$ where $\mathrm{g}$ is acceleration due to gravity on the planet. What will be escape velocity from the planet surface, if its value from moon surface is $2.5\mathrm{km}{s}^{-1}?$$\sqrt{5}=2.236?$

The escape velocity of a projectile on earth's surface is $11.2{\mathrm{kms}}^{-1}.$ A body is projected up with twice this speed. What will be the speed of the body at infinity. Ignore the presence of sun and other planet etc. 

The orbital speed of an artificial satellite orbiting very close to the earth is $8{\mathrm{kms}}^{-1}.$ What should be the increase speed of the satellite speed so that it may escape leaving its orbit?

A $500\mathrm{kg}$ artificial satellite is revolving around the earth at a height of $1800\mathrm{km}$from the earth. Find out the potential energy, kinetic energy and total energy of the satellite. The earth's radius is $6400\mathrm{km} \mathrm{and} \mathrm{g}=10{\mathrm{ms}}^{-2}.$

The mean distance of the earth from the sun is $1.496\times {10}^8\mathrm{km}$ and its sidereal revolution period is $365.3$days. The sidereal revolution period of the planets Venus and mars are $224.7$days $687.0$days respectively. Estimate the mean distance of these planets from the sun.