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Gravitation question

2019 · Q118
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Gravitation question

2019 · Q118

NEETPhysicsGravitationMCQ+4 / −1
The work done to raise a mass m from the surface of the earth to a height h, which is equal to the radius of the earth, is :
  1. A
    mgR
  2. B
    2mgR
  3. C
    12{1 \over 2}21​mgR
  4. D
    32{3 \over 2}23​mgR
View written solutionFree

Correct answer: C

Initial potential energy at Earths surface is

Ui = −GMmR - {{GMm} \over R}−RGMm​

Final potential energy at height h = R :

Uf = −GMm2R - {{GMm} \over 2R}−2RGMm​

work done = change in PE

w = Uf - Ui

= GMm2R{{GMm} \over 2R}2RGMm​

= gR2m2R{{g{R^2}m} \over {2R}}2RgR2m​

= 12{1 \over 2}21​mgR

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