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BITSAT 2010
Exam
BITSAT
Year
2010
Subject
Physics
Chapter
Gravitation

BITSAT 2010 · Physics · Gravitation

Two planets A and B have the same material density. If the radius...

Two planets A\mathrm{A} and B\mathrm{B} have the same material density. If the radius of A\mathrm{A} is twice that of B\mathrm{B}, then the ratio of the escape velocity vA/vB\mathrm{v}_{\mathrm{A}} / \mathrm{v}_{\mathrm{B}} is

Options

  1. A2
  2. B2\sqrt{2}
  3. C1/21 / \sqrt{2}
  4. D1/21 / 2

Correct answer

A. 2

Step-by-step solution

ve=2gR=2GMR2R=2Gd43πR3R2R=R2Gd43πv_{e}=\sqrt{2 g R}=\sqrt{\frac{2 G M}{R^{2}}} R=\sqrt{\frac{2 G d \frac{4}{3} \pi R^{3}}{R^{2}}} R=\mathrm{R} \sqrt{2 \mathrm{Gd} \frac{4}{3} \pi} as ve∝Rv_{e} \propto R for same density, vAvB=2\frac{v_{A}}{v_{B}}=2
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