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NEET 2016
Exam
NEET
Year
2016
Subject
Physics
Chapter
Gravitation

NEET 2016 · Physics · Gravitation

The ratio of escape velocity at earth ( υ _ e ) to the escape...

The ratio of escape velocity at earth (υe)\left({υ}_{e}\right) to the escape velocity at a planet (υp)\left({υ}_{p}\right) whose radius and mean density are twice as that of earth is:

Options

  1. A1:21: 2
  2. B1:221: 2\sqrt{2}
  3. C1:41: 4
  4. D1:21: \sqrt{2}

Correct answer

B. 1:221: 2\sqrt{2}

Step-by-step solution

vevP=2GMeRe2GMPRP=MeRPMPRe=ρe43πRe3RPρp43πRP3Re\dfrac{{v}_{e}}{{v}_{P}} = \dfrac{\sqrt{2\dfrac{G{M}_{e}}{{R}_{e}}}}{\sqrt{2\dfrac{G{M}_{P}}{{R}_{P}}}} = \sqrt{\dfrac{{M}_{e}{R}_{P}}{{M}_{P}{R}_{e}}} = \sqrt{\dfrac{{ρ}_{e}\dfrac{4}{3}\pi{R}_{e}^{3}{R}_{P}}{{ρ}_{p}\dfrac{4}{3}\pi{R}_{P}^{3}{R}_{e}}}

vevP=ρeRe2ρpRP2=12×22=122\dfrac{{v}_{e}}{{v}_{P}} = \sqrt{\dfrac{{ρ}_{e}{R}_{e}^{2}}{{ρ}_{p}{R}_{P}^{2}}} = \sqrt{\dfrac{1}{2 \times {2}^{2}}} = \dfrac{1}{2\sqrt{2}}
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