JEE Mains · Physics · STD 11 - 7. gravitation
The escape velocity of a body on a planet \('A'\) is \(12 \,kms ^{-1}\). The escape velocity of the body on another planet \('B'\) , whose density is four times and radius is half of the planet \('A'\), is ................... \(kms ^{-1}\)
- A \(12\)
- B \(24\)
- C \(36\)
- D \(6\)
Answer & Solution
Correct Answer
(A) \(12\)
Step-by-step Solution
Detailed explanation
\(V _{\text {escape }}=\sqrt{\frac{2 Gm }{ R }} \Rightarrow \sqrt{\frac{2 G \rho \times \frac{4}{3} \pi R ^{3}}{ R }}\) \(V _{\text {escape }} \propto \sqrt{\rho R ^{2}}\) \(\therefore\) if \(\rho\) is \(4\) times and Radius is halved. \(\Rightarrow V_{\text {escape }}\) will…
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