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 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…

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 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

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…

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 $\{\cos(90)^\circ = 0\}$

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

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…

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…

The kinetic energies of a planet in an elliptical orbit about the Sun, at positions, $A,B$ and $C$ are $K_{A},K_{B}andK_{C}$, respectively. $AC$ is the major axis and $SB$ is perpendicular to $AC$ at the position of the…

Kepler's third law states that the square of the period of revolution $\text{(T)}$ of a planet around the sun is proportional to the third power of the average distance $\text{r}$ between sun and planet i.e.,…

The acceleration due to gravity at a height $1 km$ above the earth is the same as at a depth $d$ below the surface of earth. Then