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 4:1
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 1
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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}{r_{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 $
BETA
