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Gravitation question

2005 · Q164
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Gravitation question

2005 · Q164

NEETPhysicsGravitationMCQ+4 / −1
Imagine a new planet having the same density as that of earth but it is 3 times bigger than the earth in size. If the acceleration due to gravity on the surface of earth is g and that on the surface of the new planet is g', then
  1. A
    g' = g/9
  2. B
    g' = 27g
  3. C
    g' = 9g
  4. D
    g' = 3g
View written solutionFree

Correct answer: D

We know that

g=GMR2=G(43πR3)R2=43πGRρg = {{GM} \over {{R^2}}} = {{G\left( {{4 \over 3}\pi {R^3}} \right)} \over {{R^2}}} = {4 \over 3}\pi GR\rho g=R2GM​=R2G(34​πR3)​=34​πGRρ

g′g=R′R=3RR=3{{g'} \over g} = {{R'} \over R} = {{3R} \over R} = 3gg′​=RR′​=R3R​=3

∴\therefore∴ g' = 3g

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