Assertion: A satellite moving in a circular orbit around the earth has a total energy E0, then its potential energy is -E0. Reason: Potential energy of the body at a point in a gravitational field of orbit is (-G M m/R).

Question

Assertion: A satellite moving in a circular orbit around the earth has a total energy E0, then its potential energy is -E0. Reason: Potential energy of the body at a point in a gravitational field of orbit is (-G M m/R). (A) If both the assertion and reason are true and reason explains the assertion. (B) If both the assertion and reason are true but reason does not explain the assertion. (C) If assertion is true but reason is false. (D) If assertion is false but reason is true.

Tardigrade Admin · Accepted Answer

Here assertion is false but reason is true For satellite. KE = (GMm/2R) and PE = (-GMm/R) Total energy, E0 = KE + PE = (GMm/2R) - (GMm/R) = (-GMm/2R) = (PE/2) PE = 2E0

Q. Assertion: A satellite moving in a circular orbit around the earth has a total energy $E_{0}$ , then its potential energy is $- E_{0}$ .
Reason: Potential energy of the body at a point in a gravitational field of orbit is $\frac{- GM m}{R}$ .

If both the assertion and reason are true and reason explains the assertion.

If both the assertion and reason are true but reason does not explain the assertion.

If assertion is true but reason is false.

If assertion is false but reason is true.

Here assertion is false but reason is true For satellite.
$K E = \frac{GM m}{2 R}$
and $PE = \frac{- GM m}{R}$
Total energy, $E_{0} = K E + PE$
$= \frac{GM m}{2 R} - \frac{GM m}{R}$
$= \frac{- GM m}{2 R} = \frac{PE}{2}$
$PE = 2 E_{0}$

Q. Assertion: A satellite moving in a circular orbit around the earth has a total energy E0​, then its potential energy is −E0​. Reason: Potential energy of the body at a point in a gravitational field of orbit is R−GMm​.