Question

Assertion :Two satellites of masses $1000$kg and $4000$kg are orbiting in the same orbit with orbital velocities in the ratio $1:2$. Reason: Orbital velocity is independent of mass of satellite.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

The reason is correct and is based on Kepler's third law. Here is an attempt of proof.

Let us call the force that the earth exert on the satellite as F.

Let us assume that the satellite is revolving around the earth in a spherical orbit of radius R. The satellite has mass m and the earth's mass is M.

Thus, $F=\frac{GMm}{R^2}$

Since the force is the centripetal force acting on the satellite which cause circular motion, $F=\frac{m{V}^2}{R}$, here $V$ is velocity of the satellite.

Now, comparing of above equations results in elimination of term m which signifies that mass of the satellite does not play any role in motion around the earth.

Now coming to assertion -

Two satellite of masses $1000kg$ and $400kg$ are orbiting in the same orbit with orbital velocities in the ratio $1:2$. These ratio is independent of mast that is exactly mentioned in the reason so we come to conclusion that assertion and reason are correct and reason is correct explanation for assertion.

Hence, the answer is both Assertion and Reason are correct and Reason is the correct explanation for assertion.