Gravitation

The kinetic energies of planets in an elliptical orbit about the Sun, at positions A, B and C are $K_A$, $K_B$ and $K_C$, respectively. AC is the major axis and SB is perpendicular to AC at the position of the Sun as…

The escape velocity of a body on the earth's surface is $v_e$. A body is thrown with a speed of $\sqrt{6}\,v_e$. Assume that the sun and the planets do not influence the motion of the body, the velocity of a body at…

Four particles of equal masses $(M)$ move along the circle of radius $R$ under the action of their mutual gravitational attraction. The magnitude of net gravitational force on each particle is $\{\cos(90)^\circ = 0\}$

The periodic time $T_1$ of a simple pendulum is $4\ \text{s}$ at a place, at a height $R$ above the earth's surface. If the pendulum is brought at a height $\dfrac{2}{3}R$ above the earth surface, the periodic time…

Imagine a new planet having the same density as that of earth, but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is $g$ and that on the surface of the planet is…

Let '$R$' be the radius of the earth. The height '$h$' from the surface of the earth where the value of acceleration due to gravity will be half its value on the surface of the earth, is

An artificial satellite is revolving around a planet in a circular orbit close to its surface. The frequency of revolution (n) of a satellite in terms of density '$\rho$' and radius 'R' of the planet is (G is the…

A planet of mass $m$ moves in an elliptical orbit around the Sun of mass $M$. Let $r_1$ be the distance at aphelion and $r_2$ be the distance at perihelion. If $v_1$ and $v_2$ are the velocities of the planet at these…

Two identical copper spheres of radius R and density $\varrho$ are placed in contact with each other. The gravitational force acting between them is proportional to $\text{R}^x$. The value of $x$ is

By how many times the energy of a satellite has to be increased to shift it from an orbit of radius 'r' to $\dfrac{5}{2}\ r$ ?

According to Kepler's second law of planetary motion, the magnitude of areal velocity $\left(\dfrac{\Delta A}{\Delta t}\right)$ of a planet of mass '$m$' revolving around the sun is constant and is equal to ('$p$' is…

Two spherical bodies of masses $M$ and $5 M$ and radii $R$ and $2 R$ are released in free space with initial separation between their centres equal to $12 R$. If they attract each other due to gravitational force only,…