The acceleration due to gravity g and density of the earth `rho` are related by which of the following relations? (where G is the gravitational constant and `R_(E)` is the radius of the earth)

Options

A. `rho=(4piGR_(E))/(3g)`
B. `rho=(3g)/(4piGR_(E))`
C. `rho=(3g)/(4pigR_(E))`
D. `rho=(4pigR_(E))/(3G)`

Answer

B

Explanation

Accleration due to gravity of earth is
`g=(GM_(E))/(R_(E)^(2))......(i)`
As `rho=(M_(E))/(4/3piR_(E)^(3)) implies M_(E)=rho4/3piR_(E)^(2)`
Subtituting this value in Eq(i), we get
`g=(G(rho4/3piR_(E)^(3)))/(R_(E)^(2))=4/3pirhoGR_(E) or rho=(3g)/(4piGR_(E))`