Question

The ratio of acceleration due to gravity on the surface
of Mercury with its value on earth's surface, assuming
that radii of Mercury and Earth are in the ratio 1:3 and
their mean densities in ratio 3:5, is

a)1:2
b)1:3
c)1:5
d)2:3​

Answer 1

Given :   radii of mercury and earth is 1:3 and their mean densities in ratio 3:5

To Find :  The ratio of acceleration due to gravity on the surface of mercury with its value on Earth's surface

Explanation:

g = GM/R²

M = Mass of Earth

R = Radius of Earth

D = Density of Earth

radii of mercury and earth is 1:3

Radii of mercury = R/3

Density = Mass / Volume

D = M / (4/3)πR³

=> M = D4πR³/3

densities in ratio 3:5

=> Density of mercury  =  3D/5

Mass of Mercury  =  (3D/5) 4π (R/3)³ /3

= D4πR³/27 * 5

= D4πR³/3 * 45

= M/45

g₁ at Mercury

g₁ = G(M/45)/(R/3)²

= GM/5R²

= g/5

g₁ : g = 1: 5

ratio of acceleration due to gravity on the surface of mercury with its value on Earth's surface  =  1 :  5

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Answer 2

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The ratio of acceleration due to gravity on the surface of Mercury with its value on earth's surface, assuming that radii of Mercury and Earth are in the ratio 1:3 and their mean densities in ratio 3:5, is

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