JEE Mains · Physics · STD 11 - 7. gravitation
Escape velocity of a body from earth is \(11.2 \mathrm{~km} / \mathrm{s}\). If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the plate is _______.
- A \(11.2 \mathrm{~km} / \mathrm{s}\)
- B (8.4 \mathrm{~km} / \mathrm{s}\)
- C \(4.2 \mathrm{~km} / \mathrm{s}\)
- D \(7.9 \mathrm{~km} / \mathrm{s}\)
Answer & Solution
Correct Answer
(D) \(7.9 \mathrm{~km} / \mathrm{s}\)
Step-by-step Solution
Detailed explanation
\(R_p=\frac{R_E}{3}, M_P=\frac{M_E}{6}\) \(V_e=\sqrt{\frac{2 G_e}{R_e}}\) \(...(1)\) \(V_p=\sqrt{\frac{2 \mathrm{GM}_p}{R_p}}\) \(....(2)\) \(\frac{V_e}{V_p}=\sqrt{2}\) \(V_P=\frac{V_e}{\sqrt{2}}=\frac{11.2}{\sqrt{2}}=7.9 \mathrm{~km} / \mathrm{sec}\)
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