Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE MainPhysicsGravitation

A geostationary satellite is orbiting the earth at a certain height. Another satellite is placed in a circular orbit such that its orbital radius is one-fourth of the orbital radius of the geostationary satellite. The time period of the second satellite is

Options

  1. A3 hours
  2. B6 hours
  3. C1.5 hours
  4. D192 hours

Correct answer

A. 3 hours

Step-by-step solution

The time period of a geostationary satellite is T₁ = 24 hours . According to Kepler's Third Law, the square of the time period is proportional to the cube of the orbital radius: T^2 R^3 Let the orbital radius of the geostationary satellite be R₁ and that of the second satellite be R₂ . We are given R₂ = R₁ 4 . Taking the ratio of their time periods: ( T₂ T₁ )^2 = ( R₂ R₁ )^3 ( T₂ 24 )^2 = ( 1 4 )^3 = 1 64 Taking the square root on both sides: T₂ 24 = 1 8 T₂ = 24 8 = 3 hours Answer: 3 hours

Practice Gravitation on Quantrex Academy →

More from Gravitation

A particle of mass m , and angular momentum is moving in a circular orbit of radius r₀ under the influence of an attractive force F (r) = - k r^2 r . Keeping its angular momentum u 2026A body of mass m is taken from the surface of earth to a height equal to twice the radius of earth ( R_e ). The increase in potential energy will be _______. ( g is acceleration du 2026When one moves from a point 16 km below the earth's surface to a point 16 km above the earth's surface. The change in g is approximately %. The value of is _____. (Take radius of t 2026The height in terms of radius of the earth (R) , at which the acceleration due to gravity becomes g 9 , where g is acceleration due to gravity on earth's surface, is ______. 2026If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and kinetic energy (k) on reaching the surface of earth. The values of v and k respectively are ___ 2026A planet (P₁) is moving around the star of mass 2M in the orbit of radius R . Another planet (P₂) is moving around another star of mass 4M in a orbit of radius 2R . Ratio of time p 2026Three masses 200 ~kg , 300 ~kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 25 2026Given below are two statements: Statement I : A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends up 2026 Full Gravitation list All JEE Main PYQs