K K Sharma Solutions for Chapter: Gravitation, Exercise 1: TOPICWISE QUESTIONS

A geostationary satellite is orbiting an Earth-like planet at a height of $5R$ above its surface with a time period of $24 \mathrm{h}$, $R$ being the radius of the planet. The time period of another satellite (in $\mathrm{hours}$) at a height of $2R$ from the surface of the planet will be

The time period of a satellite of Earth is $5 \mathrm{h}$. If the separation between the Earth and the satellite is increased to $4$ times the previous value, the new time period will become

A double star system consists of two stars $A$ and $B$ that have time periods $T_{\mathrm{A}}$ and $T_{\mathrm{B}}$, radii $r_{\mathrm{A}}$ and $r_{\mathrm{B}}$ and masses $m_{\mathrm{A}}$ and $m_{\mathrm{B}}$, respectively. Choose the correct option.

A planet is revolving around the Sun in an elliptical orbit. Its closest and farthest distance from the Sun are $r_{\min }$ and $r_{\max }$, respectively. If the orbital angular velocity of the planet when it is nearest to the Sun is $\omega$, then the orbital angular velocity at the point when it is at the farthest distance from the Sun is

A satellite of mass $m$ revolves around the Earth of radius $R$ at a height $x$ from its surface. If $g$ is the acceleration due to gravity on the surface of the Earth, then the orbital speed of the satellite is

Escape velocity of a body of $1 \mathrm{kg}$ mass on a planet is $100 \mathrm{m} {\mathrm{s}}^{-1}$. Gravitational potential energy of the body on the planet is

A missile is launched with a velocity less than the escape velocity. Sum of its kinetic energy and potential energy

What is the minimum energy required to launch a satellite of mass undefined, from the surface of a planet of mass $M$ and radius $R$, in a circular orbit at an altitude of $2R$?