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 $n$.

Which one of the following statements is true for the relation F = $\frac{G{m}_1{m}_2}{r_2}$ ?
(All symbols have their usual meanings)

The ratio of gravitational force and electrostatic repulsive force between two electrons is approximately (gravitational constant $=6.7\times {10}^{-11} \mathrm{N} {\mathrm{m}}^2 {\mathrm{kg}}^{-2}$, mass of an electron $=9.1\times {10}^{-31} \mathrm{kg}$, charge on an electron $=1.6\times {10}^{-19} \mathrm{C}$)

The gravitational force between two objects is $F$. If masses of both the objects are halved without altering the distance between them, then the gravitational force would become

A satellite is orbiting a planet in a circular orbit of radius $1\times {10}^7 \mathrm{m}.$ The gravitational force $F$ on the satellite due to the planet is $80 \mathrm{N}.$ What would be the new $F$ if the orbit radius is doubled to $2\times {10}^7 \mathrm{m}?$

A planet of density $\rho$ is rotating with time period $T$ about its own axis. Find the smallest possible time of rotation of the planet, such that a particle is remaining in contact with the planet on the equator.
$\left(\frac{3\pi }{\rho G}=4\times {10}^6 \mathrm{S}.\mathrm{I}.\mathrm{units}\right)$

A large spherical mass $M$ is fixed at one position and two identical point masses $m$ 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

The force of attraction between the earth and an object is known as

On a circle of radius $R$, four particles of equal mass $M$ move under the action of their mutual gravitational attraction. Find the speed of each particle.

In a circle of radius $R$, two particles of the equal mass move under the action of their mutual gravitational attraction. Find the speed of each particle.

Find the ratio of the gravitational pull of the earth on moon to that of the moon on earth, if the mass of moon is $1\%$ of the mass of earth.

Assertion: Gravitational force on an object on the moon is one-sixth that on the earth.
Reason: The law of gravitation is the same on both the moon and the earth.

Assume mass of Moon is $1\mathrm{\%}$ of that of the mass of Earth. Determine ratio of the mutual gravitational pull of Earth on Moon and that of Moon on Earth?

Think about Gravitational Force. Which of the following statement is correct regarding it?

Statement 1: If there exists Coulomb attraction between two bodies, both of them may not be charged. 

Statement 2: In Coulomb attraction two bodies are oppositely charged.

Choose the correct statements.

At the comers of a square of side $a$. Four identical particles each of mass $M$ are situated. What should be their speed if each of them revolves under the influence of other's gravitational field in a circular orbit circumscribing the square?

Choose the correct statements from the following:

Three masses each of mass $m$ are placed at the vertices of an equilateral triangle $\mathrm{A}\mathrm{B}\mathrm{C}$ of side $l$ as shown in figure. The force acting on a mass $2m$ placed at the centroid $\mathrm{O}$ of the triangle is