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JIPMER 2013
Exam
JIPMER
Year
2013
Subject
Physics
Chapter
Gravitation

JIPMER 2013 · Physics · Gravitation

The escape velocity for the earth is 11.2 ~km / s . The mass of...

The escape velocity for the earth is 11.2 km/s11.2 \mathrm{~km} / \mathrm{s}. The mass of another planet 100 times mass of earth and its radius is 4 times radius of the earth. The escape velocity for the planet is

Options

  1. A280 km/s280 \mathrm{~km} / \mathrm{s}
  2. B56 km/s56 \mathrm{~km} / \mathrm{s}
  3. C112 km/s112 \mathrm{~km} / \mathrm{s}
  4. D28 km/s28 \mathrm{~km} / \mathrm{s}

Correct answer

B. 56 km/s56 \mathrm{~km} / \mathrm{s}

Step-by-step solution

The escape velocity of the the planet vescape =2GmR∝MRvpve=MpRp×ReMevpve=100×14=5vp=5×11.2=56km/s\begin{aligned} v_{\text{escape }} & =\sqrt{\frac{2 G m}{R}} \propto \sqrt{\frac{M}{R}} \\ \frac{v_p}{v_e} & =\sqrt{\frac{M_p}{R_p} \times \frac{R_e}{M_e}} \\ \frac{v_p}{v_e} & =\sqrt{100 \times \frac{1}{4}}=5 \\ v_p & =5 \times 11.2=56 \mathrm{ km} / \mathrm{s}\end{aligned}
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