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Gravitation question

2021 · Q148
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Gravitation question

2021 · Q148

NEETPhysicsGravitationMCQ+4 / −1
The escape velocity from the Earth's surface is v. The escape velocity from the surface of another planet having a radius, four times that of Earth and same mass density is :
  1. A
    4υ\upsilonυ
  2. B
    υ\upsilonυ
  3. C
    2υ\upsilonυ
  4. D
    3υ\upsilonυ
View written solutionFree

Correct answer: A

ve=2GMR=2GR×43πR3ρ{v_e} = \sqrt {{{2GM} \over R}} = \sqrt {{{2G} \over R} \times {4 \over 3}\pi {R^3}\rho } ve​=R2GM​​=R2G​×34​πR3ρ​

=8πGρ3R2= \sqrt {{{8\pi G\rho } \over 3}{R^2}}=38πGρ​R2​

⇒ve∝R \Rightarrow {v_e} \propto R⇒ve​∝R

⇒veυ=4RR⇒ve=4v \Rightarrow {{{v_e}} \over \upsilon } = {{4R} \over R} \Rightarrow {v_e} = 4v⇒υve​​=R4R​⇒ve​=4v

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