MHT CET · Physics · Gravitation
The mass of earth is 81 times that of the moon and the radius of the earth is \(3.5\) times that of the moon. The ratio of the escape velocity on the surface of earth to that on the surface of moon will be
- A \(0.2\)
- B \(2.57\)
- C \(4.81\)
- D \(0.39\)
Answer & Solution
Correct Answer
(C) \(4.81\)
Step-by-step Solution
Detailed explanation
Escape velocity, \(v_{e}=\sqrt{\frac{2 G M}{R}}\)
\(\therefore\) \(\frac{v_{e}}{v_{m}}=\sqrt{\frac{M_{e} R_{m}}{M_{m} R_{e}}}\frac{v_{e}}{v_{m}}=\sqrt{\frac{81}{3.5}}=4.81\)
\(\therefore\) \(\frac{v_{e}}{v_{m}}=\sqrt{\frac{M_{e} R_{m}}{M_{m} R_{e}}}\frac{v_{e}}{v_{m}}=\sqrt{\frac{81}{3.5}}=4.81\)
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