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 $$\dfrac{E}{2}$$.
Statement II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy $$E$$.
In the light of the above statements, choose the most appropriate answer from the options given below.

We need to evaluate two statements about satellite energy.

Recall the energy relations for a satellite in orbit. For a satellite of mass $$m$$ orbiting Earth at radius $$r$$:

- Kinetic Energy: $$KE = \frac{GMm}{2r}$$

- Potential Energy: $$PE = -\frac{GMm}{r}$$

- Total Energy: $$E = KE + PE = -\frac{GMm}{2r}$$

Note that $$E$$ is negative.

Check Statement I — "PE = E/2": $$E/2 = -\frac{GMm}{4r}$$

But $$PE = -\frac{GMm}{r}$$

Since $$PE \neq E/2$$ (in fact, $$PE = 2E$$), Statement I is incorrect.

Check Statement II — "KE = |E|/2": $$|E| = \frac{GMm}{2r}$$

$$|E|/2 = \frac{GMm}{4r}$$

But $$KE = \frac{GMm}{2r} = |E|$$

Since $$KE = |E| \neq |E|/2$$, Statement II is incorrect.

The correct relationships are: $$PE = 2E$$ and $$KE = -E = |E|$$.

Since both statements are incorrect, the correct answer is Option D: Both Statement I and Statement II are incorrect.