R is the radius of the earth and g is the acceleration due to gravity on the earth’s surface, then the density of the earth isa.3gR/4πGb.3G/4gπRc.3g/4πGRd.4g/3πGR
Question
R is the radius of the earth and g is the acceleration due to gravity on the earth’s surface, then the density of the earth isa.3gR/4πGb.3G/4gπRc.3g/4πGRd.4g/3πGR
Solution
The density (D) of the Earth can be calculated using the formula:
D = Mass/Volume
We know that the mass (M) of the Earth can be calculated using the formula:
M = gR^2/G
where:
- g is the acceleration due to gravity on the Earth's surface
- R is the radius of the Earth
- G is the gravitational constant
The volume (V) of the Earth can be calculated using the formula for the volume of a sphere:
V = 4/3πR^3
Substituting these equations into the formula for density gives:
D = (gR^2/G) / (4/3πR^3)
Simplifying this equation gives:
D = 3g / (4πGR)
So, the correct answer is c. 3g/4πGR.
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