Gravitation Questions

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, the orbital speed of the satellite is:

The time period of an earth satellite in circular orbit is independent of:

If $g$ is the acceleration due to gravity on the earth’s surface, the gain in the potential energy of object of mass $m$ raised from the surface of the earth to a height equal to the radius $R$ of the earth is:

Suppose the gravitational force varies inversely as the $n^{th}$ power of distance. Then the time period of a planet in circular orbit of radius $R$ around the sun will be proportional to:

Average density of the earth:

The change in the value of $g$ at a height ‘$h$ ’ above the surface of the earth is the same as at a depth ‘$d$ ’ below the surface of earth. When both ‘$d$ ’ and ‘$h$ ’ are much smaller than the radius of earth, then which one of the following is correct?

A particle of mass $10\text{ g}$ is kept on the surface of a uniform sphere of mass $100\text{ kg}$ and radius $10\text{ cm}$. Find the work to be done against the gravitational force between them to take the particle far away from the sphere [$G=6.67\times 10^{-11}{\text{ Nm}}^2/{\text{kg}}^2$ ]:

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

The escape velocity for a body projected vertically upwards from the surface of earth is $11\text{km/s}$. If the body is projected at an angle of $45^{\circ }$ with the vertical, the escape velocity will be:

Two spherical bodies of mass $M$ and $5M$ and radii $R$ and $2R$ respectively are released in free space with initial separation between their centres equal to $12R$. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is:

A planet in a distant solar system is $10$ times more massive than the earth and its radius is $10$ times smaller. Given that the escape velocity from the earth is $11\text{km/s}$, the escape velocity from the surface of the planet would be:

Statement - 1: For a mass $M$ kept at the centre of a cube of side ‘$a$ ’, the flux of gravitational field passing through its sides is $4\pi GM$.Statement - 2: If the direction of a field due to a point source is radial and its dependence on the distance ‘$r$ ’ for the source is given as $1/r^2$, its flux through a closed surface depends only on the strength of the source enclosed and not on the size or shape of the surface.

The height at which the acceleration due to gravity becomes $g/9$ (where $g=$ the acceleration due to gravity on the surface of the earth) in terms of $R$, the radius of the earth is:

Two bodies of masses $m$ and $4m$ are placed at a distance $r$. The gravitational potential at a point on the line joining them where the gravitational field is zero is:

The mass of a spaceship is $1000\text{kg}$. It is to be launched from the earth's surface out into free space. The value of '$g$ ' and '$R$ ' (radius of earth) are $10{\text{m/s}}^2$ and $6400\text{km}$ respectively. The required energy for this work will be: