Gravitation Question 249

Question: Two identical satellites are at R and 7R away from earth surface, the wrong statement is (R = Radius of earth) [RPMT 1997]

Options:

A) Ratio of total energy will be 4

B) Ratio of kinetic energies will be 4

C) Ratio of potential energies will be 4

D) Ratio of total energy will be 4 but ratio of potential and kinetic energies will be 2

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Answer:

Correct Answer: D

Solution:

Orbital radius of satellites $ [r_{1}=R+R=2R] $

$ [r_{2}=R+7R=8R] $

$ [U_{1}=\frac{-GMm}{r_{1}}] $

and $ [U_{2}=\frac{-GMm}{r_{2}}] $ $ [K_{1}=\frac{GMm}{2r_{1}}] $

and $ [K_{2}=\frac{GMm}{2r_{2}}] $ $ [E_{1}=\frac{GMm}{2r_{1}}] $

and $ [E_{2}=\frac{GMm}{2r_{2}}] $ $ [\frac{U_{1}}{U_{2}}=\frac{K_{1}}{K_{2}}=\frac{E_{1}}{E_{2}}=4] $



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