Gravitation

JEE Main level, single correct, medium

121 of 223

Question 121 of 223

Given below are two statements:
Statement I: IfEEbe the total energy of a satellite moving around the earth, then its potential energy will be E2\dfrac{E}{2}.
Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy EE.
In the light of the above statements, choose the most appropriate answer from the options given below.

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Answer: (D) Both Statement I and Statement II are incorrect

Let mm be the mass of the satellite.
The potential energy of the satellite is
U=−GMmrU=\dfrac{-GMm}{r}
The velocity of the satellite is given by
v=GMrv=\sqrt{\dfrac{GM}{r}}
Kinetic energy is given by
K=mv22=m2GMr=GMm2rK=\dfrac{m{v}^{2}}{2}=\dfrac{m}{2}\dfrac{GM}{r}=\dfrac{GMm}{2r}
The total mechanical energy is the sum of potential and kinetic energy. So,
T=K+U=GMm2r−GMmr=−GMm2rT=K+U=\dfrac{GMm}{2r}-\dfrac{GMm}{r}=-\dfrac{GMm}{2r}
Hence, both the statements are false.

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