P.E = 2 T.E =>P.E = 2E0 ln case of circular motion of satellite around the earth / planet revolving around the sun / electrones revolving in circular orbit P. E = 2T.E and |K E| = | T.E |

The correct answer is option 'C' - 2E0.

Explanation:

1. Understanding the energy of a satellite in a circular orbit:
When a satellite is in a circular orbit around the Earth, it experiences both kinetic energy and potential energy. The total energy of the satellite is the sum of these two energies.

2. Kinetic energy of the satellite:
The kinetic energy of the satellite is given by the formula:
KE = (1/2)mv^2
where m is the mass of the satellite and v is its velocity.

In a circular orbit, the satellite moves with a constant speed, which is determined by the gravitational force between the satellite and the Earth. This speed is given by the formula:
v = √(GM/r)
where G is the gravitational constant, M is the mass of the Earth, and r is the radius of the orbit.

Substituting this value of velocity into the equation for kinetic energy, we get:
KE = (1/2)m(√(GM/r))^2
= (1/2)m(GM/r)
= GMm/2r

3. Potential energy of the satellite:
The potential energy of the satellite is given by the formula:
PE = -GMm/r
Note that the potential energy is negative because the satellite is in a bound orbit.

4. Total energy of the satellite:
The total energy of the satellite is the sum of its kinetic energy and potential energy:
E0 = KE + PE
= GMm/2r - GMm/r
= -GMm/2r

5. Conclusion:
From the equation for the total energy, we can see that the potential energy is equal to -GMm/2r. Therefore, the potential energy of the satellite is -E0/2. However, the question asks for the potential energy alone, not its negative value. So, the potential energy of the satellite is E0/2.

Thus, the correct answer is option 'C' - 2E0.