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 E/2.
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

Solution

Physics sir · 4 steps

Write KE, PE and E for a circular orbit in terms of GMm/2r, then compare each with E.

1. Orbital speed. Gravity supplies the centripetal force, so mv²/r = GMm/r². This gives mv² = GMm/r.

   Quantity	Formula	In terms of E
   Kinetic energy K	1/2mv² = +GMm/2r	K = -E = |E|
   Potential energy U	-GMm/r	U = 2E
   Total energy E	K + U = -GMm/2r	E

2. Check Statement I. It says U = E/2. In fact U = -GMm/r is twice E = -GMm/2r, so U = 2E. Statement I is incorrect.
3. Check Statement II. It says K = |E|/2. In fact K = GMm/2r, which is equal to |E| itself, not half of it. Statement II is incorrect.
4. So. Both statements are wrong, and the answer is (a).

The idea to keep. For any circular orbit, remember the ratio K : U : E = 1 : -2 : -1. Then U = 2E and K = -E follow at once.

Answer from the NTA final answer key. Solution by PrepWiser.