JEE Physics 2023 Question with Solution

Given: Two statements about the energy of a satellite revolving around the Earth.

Find: Which statement is correct.

For a satellite in a circular orbit, the standard energy relations are:

$$PE = -2KE$$

and

$$E = KE + PE = KE - 2KE = -KE$$

So,

$$KE = -E = |E|$$

and also

$$PE = 2E$$

because $E$ is negative.

Now analyze the statements:

1. Statement I: It says potential energy is $\frac{E}{2}$. But from the orbital energy relation,

$$PE = 2E$$

So Statement I is incorrect.

2. Statement II: It says kinetic energy is equal to half the magnitude of total energy. But actually,

$$KE = |E|$$

not

$$KE = \frac{|E|}{2}$$

So Statement II is also incorrect.

Therefore, both statements are incorrect. The correct option is A.

Given:

• $E = KE + PE$
• $PE = -2KE$

Find: Truth values of Statement I and Statement II.

Substitute $PE = -2KE$ into total energy:

$$E = KE + (-2KE)$$ $$E = -KE$$

Hence,

$$KE = -E = |E|$$

Now use $PE = -2KE$:

$$PE = -2|E|$$

Since $E < 0$ for a bound satellite orbit, this is equivalently written as

$$PE = 2E$$

Therefore:

• Statement I is false because it gives $PE = \frac{E}{2}$ instead of $PE = 2E$.
• Statement II is false because it gives $KE = \frac{|E|}{2}$ instead of $KE = |E|$.

Therefore, both statements are incorrect. The correct option is A.