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A planet has twice the density of earth but the acceleration due to gravity on its surface is exactly the same a on the surface of earth. Its radius in terms of radiusof earth R will be

A planet has twice the density of earth but the acceleration due to gravity on its surface is exactly the same a on the surface of earth. Its radius in terms of radiusof earth R will be

Grade:10

1 Answers

Sanju
106 Points
3 years ago
We have, g = GM / R^2.....
Since density  = mass / volume, we can write mass, M = density * volume.
Therefore, g = [G*density*volume] / R^2
Substituting volume = 4/3 * pi * R^3 in tha above eqn..
So g = [4/3 * pi * R^3 * G * density] / R^2 =  4/3 * pi * R * G * density
 
Therefore, ratio of radius of planet to that of earth is:
R(planet) / R(earth) = Density(earth) / Density(planet) = ½
or R(planet) = R(earth) / 2
So the answer is R/2, where R is the radius of earth

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