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

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