Q107 / 150 · MHT CET 2011 · Physics

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
    $2.57$
  • Correct answer
    C
    $4.81$
  • D
    $0.39$

Solution

Escape velocity, $v_{e}=\sqrt{\frac{2 G M}{R}}$ $\therefore$ $$ \frac{v_{e}}{v_{m}}=\sqrt{\frac{M_{e} R_{m}}{M_{m} R_{e}}} \frac{v_{e}}{v_{m}}=\sqrt{\frac{81}{3.5}}=4.81 $$

Hence, the correct answer is option: 'C'.

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