JEE Mains · Physics · STD 11 - 7. gravitation
A planet having mass \(9\,Me\) and radius \(4 R _e\), where Me and \(\operatorname{Re}\) are mass and radius of earth respectively, has escape velocity in \(km / s\) given by:(Given escape velocity on earth \(\left.V_e=11.2 \times 10^3\,m / s \right)\)
- A \(67.2\)
- B \(16.8\)
- C \(33.6\)
- D \(11.2\)
Answer & Solution
Correct Answer
(B) \(16.8\)
Step-by-step Solution
Detailed explanation
\(V_p=\sqrt{\frac{2 G_p}{R_p}} V_E=\sqrt{\frac{2 GM _E}{R_E}}\) \(\frac{V_P}{V_E}=\frac{\sqrt{\frac{2 G_P}{R_p}}}{\sqrt{\frac{2 G_E}{R_E}}}=\sqrt{\frac{R_E}{R_P} \times \frac{M_P}{M_E}}\) \(V_P=\sqrt{\frac{1}{4} \times 9} \times V_E=\frac{3}{2} V_E\)…
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