Gravitation Question 322

Question: 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

Options:

A) $ [g’=g/9] $

B) $ [g’=27g] $

C) $ [g=9g] $

D) $ [g’=3g] $

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Answer:

Correct Answer: D

Solution:

  • We know that $ [g=\frac{GM}{R^{2}}=\frac{G\left( \frac{4}{3}\pi R^{3} \right)\rho }{R^{2}}=\frac{4}{3}g\pi GR\rho ] $

    $ [\frac{g’}{g}=\frac{R’}{R}=\frac{3R}{R}=3\therefore g’=3g] $



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