Given below are two statements: Statement I: If   E   be the total energy of a satellite moving…

Given below are two statements:

Statement I: If E be the total energy of a satellite moving around the earth, then its potential energy will be  E2.

Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy E.

In the light of the above statements, choose the most appropriate answer from the options given below.

  1. Statement I is correct but Statement II is incorrect
  2. Statement I is incorrect but Statement II is correct
  3. Both Statement I and Statement II are correct
  4. Both Statement I and Statement II are incorrect

Solution

Let m be the mass of the satellite.

The potential energy of the satellite is 

U=-GMmr

The velocity of the satellite is given by 

v=GMr

Kinetic energy is given by

K=mv22=m2GMr=GMm2r

The total mechanical energy is the sum of potential and kinetic energy. So,

T=K+U=GMm2r-GMmr=-GMm2r

Hence, both the statements are false.

Asked in: JEE Main 2023 (08 Apr Shift 1)

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