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Gravitation · Question 13

JEE Main 2025 (Online) 4th April Evening ShiftMCQEasy📈 Topic in 13% papers+4−1
1

An object is kept at rest at a distance of 3R above the earth's surface where R is earth's radius. The minimum speed with which it must be projected so that it does not return to earth is : (Assume M = mass of earth, G = Universal gravitational constant)

  1. 3GMR
  2. 2GMR
  3. GM2R
  4. GMR

Answer

(3) GM2R

Solution

Distance of the object from the centre of the earth: r = R + 3R = 4R

To escape (not return), its total mechanical energy must be at least zero:

12mv2 - GMm4R = 0

v2 = 2GM4R = GM2R

v = GM2R

Answer: (3)

JEE Main 2025 (Online) 4th April Evening Shift

Keep practising — Gravitation

2

Three identical spheres of mass m are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time T = 4 seconds. If the sides of the triangle are increased to length 2a and also the masses of the spheres are made 2 m, then they will collide after seconds.

JEE Main 2025 (Online) 3rd April Morning Shift
3

A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is 1010 J. (Mass of earth = 6 1024 kg, Radius of earth = 6.4 106 m, Gravitational constant = 6.67 10-11 N m2 kg-2)

JEE Main 2025 (Online) 2nd April Evening Shift
4

Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be:

  1. 8.4
  2. 11.2
  3. 5.6
  4. 2.8
JEE Main 2025 (Online) 28th January Evening Shift

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