JEE Mains · Physics · STD 11 - Gravitation
- JEE Mains 2020
- Medium
- Numerical
Planet \(A\) has mass \(\mathrm{M}\) and radius \(\mathrm{R}\). Planet \(\mathrm{B}\) has half the mass and half the radius of Planet \(A\). If the escape velocities from the Planets \(A\) and \(\mathrm{B}\) are \(v_{\mathrm{A}}\) and \(v_{\mathrm{B}},\) respectively, then \(\frac{v_{\mathrm{A}}}{v_{\mathrm{B}}}=\frac{\mathrm{n}}{4}\) The value of \(\mathrm{n}\) is
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Answer & Solution
Correct Answer
(A) \(4\)
Step-by-step Solution
Detailed explanation
\(\mathrm{V}_{\mathrm{e}}=\sqrt{\frac{2 \mathrm{GM}}{\mathrm{R}}}\) (Escape velocity)
\(V_{A}=\sqrt{\frac{2 G M}{R}}\)
\(V_{B}=\sqrt{\frac{2 G[M / 2]}{R / 2}}=\sqrt{\frac{2 G M}{R}}\)
\(\frac{\mathrm{V}_{\mathrm{A}}}{\mathrm{V}_{\mathrm{B}}}=1=\frac{\mathrm{n}}{4} \Rightarrow \mathrm{n}=4\)
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