JEE Mains · Physics · STD 11 - 7. gravitation
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 :
- 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
Answer & Solution
Correct Answer
(B) Statement \(I\) is correct but statement \(II\) is incorrect
Step-by-step Solution
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 \(R\) \(\Rightarrow\)…
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