JEE 2021 | Gravitation

The value of acceleration due to gravity at Earth’s surface is 9.8 ms^-2. The altitude above its surface at which the acceleration due to gravity decreases to 4.9 ms^-2, is close to : (Radius of earth = 6.4 × 10⁶ m)

A test particle is moving in a circular orbit in the gravitational field produced by a mass density . Identify the correct relation between the radius R of the particle’s orbit and its period T:

Four identical particles of mass M are located at the corners of a square of side ’a'. What should be their speed if each of them revolves under the influence of others' gravitational field in a circular orbit circumscribing the square?

A man can jump over b = 4 m wide trench on earth. If mean density of an imaginary planet is twice that of the earth, calculate its maximum possible radius so that he may escape from it by jumping. (Given radius of earth, R = 6.4 × 10⁶ m)

A thin spherical shell of total mass M and radius R is held fixed. There is a small hole in the shell. A mass m is released from rest at a distance R from the hole along a line that passes through the hole and also through the centre of the shell. This mass subsequently moves under gravitational force of the shell. How long does the mass take to travel from the hole to the point diametrically opposite on the shell?

A satellite is revolving in a circular orbit very close to the surface of a planet. At some point it is given an impulse along its direction of motion, causing its velocity to increase η times. It now goes into an elliptical orbit. The maximum possible value of η for this to occur is

Consider two satellites A & B of equal mass m, moving in same circular orbit about earth, but in opposite sense as shown in figure. The orbital radius is r. The satellites undergoes a collision which is perfectly inelastic. For this situation mark the INCORRECT statement(s) – Take mass of earth as M.