Assignment

Two particles of masses $m$ and $M$ are placed at a distance $r.$ The ratio of gravitational force on mass $m$ due to mass $M$ and on mass $M$ due to mass $m$ is

The variation of acceleration due to gravity of earth as one moves away from earth's center to surface of earth is given by (Where $R$ is radius of earth)

A particle is projected vertically upwards with a speed of $\sqrt{gR}$ from earth's surface. The maximum height attained by it is (Where $R$ is the radius of earth)

A particle is projected vertically upwards from the surface of earth (radius of earth is $R$ ) with a kinetic energy equal to one fourth of the minimum value needed for it to escape. The height to which it rises above the surface of earth is

The distance of two planets from the sun are ${10}^{12} \mathrm{m}$ and ${10}^{11} \mathrm{m}.$ The ratio of their time period is

The escape speed of a projectile on earth's surface is $11.2 \mathrm{km} {\mathrm{s}}^{-1}.$ A body is projected out with twice of this speed. The speed of body far away from the earth is (Ignore the presence of other bodies)

Two planets have the same average mass density but their radii are in the ratio $1: 2$. The ratio of their respective acceleration due to gravity is

A satellite revolving around earth has kinetic energy $E_0,$ then its potential energy and total energy will be