Correct formula for height of a satellite from earth's surface is: (a) ((T²R²g)/(4π²))1/3 -R (b) ((T²R²g)/(4π))1/2 -R (c) ((T²R²g)/(4π²))-1/3 +R (d) ((T²R²)/(4π²g))1/3 -R

Answer: (a). Kepler's law: T² = (4π² r³)/(GM) with r = R + h. Use GM = gR²: r³ = (T² g R²)/(4π²). h = r - R = ((T²R²g)/(4π²))1/3 - R So the answer is (a).

Correct formula for height of a satellite from earth's surface is: | JEE Main 2024 (4 Apr, Shift 2)

Q21JEE Main 2024 · 4 APR · SHIFT 2Easy

Satellites - Orbital Velocity & Period

Correct formula for height of a satellite from earth's surface is:

Show answer and solution

Answer: (a)

Kepler's law: $T^2 = \frac{4\pi^2 r^3}{GM}$ with $r = R + h$ .
Use $GM = gR^2$ : $r^3 = \frac{T^2 g R^2}{4\pi^2}$ .
$h = r - R = \left(\frac{T^2R^2g}{4\pi^2}\right)^{1/3} - R$
So the answer is (a).

Report a mistake

More questions on Satellites - Orbital Velocity & Period

A small planet is revolving around a very massive star in a circular orbit of radius ' R…MHT CET 2024 (10 May, Shift 1)
A light planet is revolving around a massive star in a circular orbit of radius R with a…JEE Main 2024 (1 Feb, Shift 2)
A satellite revolving around a planet in stationary orbit has time period 6 hours. The…JEE Main 2024 (5 Apr, Shift 2)
A satellite of mass ' m ' is revolving around the earth of mass ' M ' in an orbit of…MHT CET 2024 (15 May, Shift 1)
Assuming that the earth is revolving around the sun in circular orbit of radius R, the…MHT CET 2024 (11 May, Shift 1)
Two planets A and B having masses m₁ and m₂ move around the sun in circular orbits of r₁…JEE Main 2024 (8 Apr, Shift 1)
A satellite moves in a stable circular orbit round the earth if (where VH, Vc and Ve are…MHT CET 2023 (10 May, Shift 1)
Two satellites A and B move round the earth in the same orbit. The mass of A is twice the…JEE Main 2023 (12 Apr, Shift 1)

Satellites - Orbital Velocity & Period question from JEE Main 2024 (4 Apr, Shift 2)

More questions on Satellites - Orbital Velocity & Period