Question

Assertion :If we double the circular radius of a satellite, then its potential energy, kinetic energy and total mechanical energy will become half Reason: Orbital speed of a satellite $v\propto \frac{1}{\sqrt{r}}$ where $r$ is its radius of orbit

• 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 B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Assertion is correct. Since, $\frac{m{v}^2}{R}=\frac{GMm}{R^2}\Rightarrow v=\sqrt{\frac{GM}{R}}$, reason is also correct. But the reason is not complete enough to explain the assertion. This is because the reason does not say anything about the potential energy of the planet. The potential energy of the planet is inversely proportional to the radius of the orbit $R$. Therefore, when radius of orbit is doubled, kinetic, potential and total mechanical energies are halved. So assertion and reason are correct but reason does not explain the assertion.