B M Sharma Solutions for Chapter: Gravitation, Exercise 6: Exercises

The gravitational force between two objects were proportional to $\frac{1}{R}$ (and not as $\frac{1}{R^2}$), where $R$ is the distance between them, then a particle in a circular path (under such a force) would have its orbital speed $v,$ proportional to

Two particles of equal mass go round a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is -

The radius of a planet is $R$. A satellite revolves around it in a circle of radius $r$ with angular velocity ${\omega }_0$. The acceleration due to the gravity on planet's surface is

A sky laboratory of mass $3\times {10}^3\mathrm{}\mathrm{k}\mathrm{g}$ has to be lifted from one circular orbit of radius $2R$ into another circular orbit of radius $3R$. Calculate the minimum energy (in $\times {10}^{10}\mathrm{J}$) required if the radius of earth is $R=6.4\times {10}^6\mathrm{m}$ and $g=10\mathrm{m}{\mathrm{s}}^{-2}$.

The gravitational field in a region is given by $\overrightarrow{E}=\left(3\widehat{i}-4\widehat{j}\right)\mathrm{}\mathrm{N}\mathrm{}\mathrm{k}{\mathrm{g}}^{-1}$. Find out the work done (in joule) in displacing a particle by $1\mathrm{}\mathrm{m}$ along the line $4y=3x+9$.

A man can throw a ball at a speed on the earth which can cross a river of width $10 \mathrm{m}$. The man reaches an imaginary planet whose mean density is twice that of the earth. Find out the maximum possible radius of the planet (in $\mathrm{k}\mathrm{m}$) so that if the man throws the ball at the same speed it may escape from the planet. Given the radius of the earth $=6.4\times {10}^6 \mathrm{m}$.

The earth is assumed to be a sphere of radius $R$. A platform is arranged at a height $3R$ from the surface of the earth. The escape velocity of a body from this platform is $f{v}_e$ where $v_e$ is its escape velocity from the surface of the earth. Find the value of $f$.

An artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of escape velocity from the earth. If the satellite is stopped suddenly in its orbit and allowed to fall freely onto the earth, find the speed (in $\mathrm{m}/\mathrm{s}$) with which it hits the surface of the earth.