Newton's Law of Gravitation

Two point masses of mass $4m$ and $m$, respectively, separated by distance $d$ are revolving under mutual force of attraction. The ratio of their kinetic energies will be

A mass is at the centre of a square, with four masses at the corners as shown: 

Rank the choice according to the magnitude of the gravitational force of the center mass. 

A satellite is launched in the equatorial plane in such a way that it can transmit signals up to $60°$ latitude on the earth. The angular velocity of the satellite is $\sqrt{\frac{GM}{n{R}^3}}$. Find $n$.

_____ (Air Resistance/Gravitational/Natural) force is the source of centripetal force that a planet requires revolving around the Sun.

Which of Kepler's Laws of planetary motion led Newton to establish the inverse-square rule for the gravitational force between two bodies?

The centripetal force acting on a satellite revolving around the earth is $\mathrm{F}$. The gravitational force on that planet is also $\mathrm{F}$. The resultant force on the satellite is

Derive the inverse relation of the gravitational force between two bodies using Kepler's law. 

The ratio of electrostatic force and gravitational force between a proton and an electron is

If the distance between two masses is doubled, the gravitational attraction between them is..

Suppose the acceleration due to gravity at the Earth's surface is $10 \mathrm{m} {\mathrm{s}}^{-2}$ and at the surface of Mars it is $4.0 \mathrm{m} {\mathrm{s}}^{-2}$. A $60 \mathrm{kg}$ passenger goes from the Earth to Mars in a spaceship moving with a constant velocity. Neglect all other objects in the sky. Which part of the given figure best represents the weight (net gravitational force of the passenger) as a function of time?

The ratio of magnitude of electrostatic force and gravitational force acting between an electron and a proton is

In Cavendish's experiment

A star of mass $M$ and radius $R$ is made up of gases. The average gravitational pressure compressing the star due to gravitational pull of the gases making up the star depends on $R$ as

In Cavendish's experiment why lead ball was used?

Experimentally the value of universal gravitational constant $\left(\mathrm{G}\right)$ was measured by 

The magnitude of the gravitational force experienced by a small spaceship of mass $M$ inside an inter-galactic dust cloud (assumed to be spherically symmetric but not necessarily uniform) when it is at a distance of $r$ from the center of the cloud is found to be

$F\left(r\right)=\alpha r+\frac{\beta }{r}.$

The density of the dust cloud is ( $G$ is Newton's gravitational constant)

A body weighs $200\mathrm{ }\mathrm{N}$ on the surface of the earth. How much will it weigh half way down to the centre of the earth?

Two stars of masses $m_{\mathit{1}}$ and $m_{\mathit{2}}$ are part of a binary star system. The radii of their orbits are $r_{\mathit{1}}$ and $r_{\mathit{2}}$ respectively, measured from the centre of mass of the system. The magnitude of gravitational force $m_{\mathit{1}}$ exerts on $m_{\mathit{2}}$ is

Two identical spheres each of mass $M$ and radius $R$ are separated by a distance $10R$. The gravitational force on mass $m$ placed at the midpoint of the line joining the centres of the spheres is 

An astronaut of mass $m$ is working on a satellite orbiting the earth at a distance $h$ from the earth's surface. The radius of the earth is $R$, while its mass is $M$. The gravitational pull $F_G$ on the astronaut is