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 on :

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(B) Statement \(I\) is correct but statement \(II\) is incorrect

Detailed explanation

\(V _{ e }=\sqrt{\frac{2 GM }{ R }} \Rightarrow V _{ e } \propto \sqrt{\frac{ M }{ R }}\)

As \(\frac{M}{R}\) increases \(\Rightarrow V_e\) increases

Statement \((1)\) is correct

Also \(V _{ e } \propto \frac{1}{\sqrt{ R }}\)

As \(V _{ e }\) depends upon \(R\)

\(\Rightarrow\) Statement \((2)\) is incorrect

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