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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

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

Answered by Thiyagarajan K | 18 Apr, 2024, 07:52: AM
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