NEET Class neet Answered
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 of the new planet is g', then
relationship between g and g' is
Asked by gouranshi84 | 17 Apr, 2024, 05:23: PM
Expert Answer
Acceleration due to gravity g = G ( M / R2 ) ..................(1)
where G is universal gravitational constant , M is mass of earth and R is radius of earth .
If ρ is density of earth , then mass M = volume × density = (4/3)πR3 × ρ
Hence eqn.(1) is rewritten as
g = [ (4/3)π G ] R × ρ
From above expression, we see that acceleration due to gravity is directly proportional to radius R and
also directly proportional to density ρ .
Let g' be the acceleration due to gravity of new planet that has size three times of earth.
If earth and new planet has same density , then their ratio of acceleration due to gravities is
( g / g' ) = R/ (3R) = 1/3
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