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. 

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?

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)

Ratio of inertial mass to gravitational mass of a body is

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

A large sphere of mass $M$ is fixed at one position and two identical particles each of mass $m$ are kept on a line passing through the centre of $M$ (see figure). The point masses are connected by a rigid massless rod of length $l$ and this assembly is free to move along the line connecting them. All three masses interact only through their mutual gravitational interaction. When the point mass nearer to $M$ is at a distance $r=3l$ from $M$, the tension in the rod is zero for $m=k\left(\frac{M}{288}\right)$. The value of $k$ is

A system of binary stars of masses $M_1$ and $M_2$ are moving in circular orbits of radii $r_1$ and $r_2$ respectively. If $T_1$ and $T_2$ are the time periods of revolution of masses $M_1$ and $M_2$ respectively and if $\frac{r_1}{r_2}=2,$ then find $\frac{T_1}{T_2}.$