Given below are two statements :
Statement I: For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases.
Statement II: Escape velocity is independent of the radius of the planet.
In the light of above statements, choose the most appropriate answer from the options given below.
Select the correct option:
A
Both Statement I and Statement II are incorrect
B
Statement I is correct but statement II is incorrect
C
Statement I is incorrect but statement II is correct
D
Both Statement I and Statement II are correct
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Sol.
$$
\begin{aligned}
& V_e=\sqrt{\frac{2 G M}{R}} \Rightarrow V_e \propto \sqrt{\frac{M}{R}} \\
& \text { As } \frac{M}{R} \text { increases } \Rightarrow V_e \text { increases }
\end{aligned}
$$
Statement (1) is correct
Also $\mathrm{V}_{\mathrm{e}} \propto \frac{1}{\sqrt{\mathrm{R}}}$
As $\mathrm{V}_{\mathrm{e}}$ depends upon R
⇒ Statement (2) is incorrect Option (2) is correct
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