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Question: The acceleration due to gravity ‘g’ and mean density of the earth r are related by which of the foll...

The acceleration due to gravity ‘g’ and mean density of the earth r are related by which of the following relations ? (Where G is the gravitational constant and R is radius of earth)

A

r = 4πgR23G\frac { 4 \pi \mathrm { gR } ^ { 2 } } { 3 \mathrm { G } }

B

r = 4πgR33G\frac { 4 \pi \mathrm { gR } ^ { 3 } } { 3 \mathrm { G } }

C

r = 3 g4πGR\frac { 3 \mathrm {~g} } { 4 \pi \mathrm { GR } }

D

r = 3G4πGR3\frac { 3 \mathrm { G } } { 4 \pi \mathrm { GR } ^ { 3 } }

Answer

r = 3 g4πGR\frac { 3 \mathrm {~g} } { 4 \pi \mathrm { GR } }

Explanation

Solution

g =

g =

g = 43\frac { 4 } { 3 }pGRr ̃ r = 3 g4πGR\frac { 3 \mathrm {~g} } { 4 \pi \mathrm { GR } }