The radii of two planets are R and 2R respectively and their densities and /2respectively. What is the ratio of acceleration due to gravity at their surfaces?
Question
The radii of two planets are R and 2R respectively and their densities and /2respectively. What is the ratio of acceleration due to gravity at their surfaces?
Solution
The acceleration due to gravity on the surface of a planet is given by the formula:
g = GM/R^2
where G is the gravitational constant, M is the mass of the planet, and R is the radius of the planet.
The mass of a planet is given by its volume times its density, so M = 4/3 * π * R^3 * ρ. Substituting this into the formula for g gives:
g = G * 4/3 * π * R^3 * ρ / R^2 = 4/3 *
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