Match List I with List II (where $a$ = radius of planet orbit, $r$ = radius of planet, $M$ = mass of Sun, $m$ = mass of planet):
$$\begin{array}{|l|l|l|l|}\hline & \text{List I} & & \text{List II} \\ \hline \text{A.} & \text{Kinetic energy of planet} & \text{I.} & -\dfrac{GMm}{a} \\ \hline \text{B.} & \text{Gravitational potential energy of sun-planet system} & \text{II.} & \dfrac{GMm}{2a} \\ \hline \text{C.} & \text{Total mechanical energy of planet} & \text{III.} & \dfrac{Gm}{r} \\ \hline \text{D.} & \text{Escape energy at the surface of planet for unit mass object} & \text{IV.} & -\dfrac{GMm}{2a} \\ \hline \end{array}$$
Choose the correct answer from the options given below:
Answer: (B) (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
For a circular orbit of radius $a$:
- Kinetic energy $= \dfrac{GMm}{2a}$ → (II)
- Potential energy $= -\dfrac{GMm}{a}$ → (I)
- Total energy $= -\dfrac{GMm}{2a}$ → (IV)
- Energy needed per unit mass to escape from the planet's surface $= \dfrac{Gm}{r}$ → (III)
Solution by Sreeraj P, M.Sc Physics