If G is Universal gravitational constant and R is the radius of the earth, then acceleration due to gravity g and the mean density of earth D are related by the equation :

Open in App

Solution

Suppose,
Mass of earth is M, radius of earth is R.
Density of earth is, D = M/[(4/3)Ï€R³]
=> M = (4/3)Ï€R³D
Now, g = GM/R²
=> g = G Ã— (4/3)Ï€R³D Ã— (1/R²)
=> g = G Ã— (4/3)Ï€RD
=> g = (4/3)Ï€GRD

Suggest Corrections

Similar questions

Acceleration due to gravity 'g' in terms of mean density of the Earth, 'd ' (where R is radius of the Earth and G is universal gravitational constant) is

The acceleration due to gravity g and the mean density of earth p are related by which relation.?

{G=gravitational constant, R= radius of earth{

Q. The acceleration due to gravity

g

and density of the earth

ρ

R_{E}

is the radius of the earth)

Q. The acceleration due to gravity 'g' for objects on or near the surface of earth is related to the universal gravitational constant 'G' as ( 'M' is the mass of the earth and 'R' is its radius ) __________________.

Q. Pick out the correct relation(s) between universal gravitational constant

(G)

and acceleration due to gravity

(g)

M = mass of earth,
R = radius of earth.

Join BYJU'S Learning Program

If G is Universal gravitational constant and R is the radius of the earth, then acceleration due to gravity g and the mean density of earth D are related by the equation :

Suppose,Mass of earth is M, radius of earth is R.Density of earth is, D = M/[(4/3)Ï€R3]=> M = (4/3)Ï€R3DNow, g = GM/R2=> g = G Ã— (4/3)Ï€R3D Ã— (1/R2)=> g = G Ã— (4/3)Ï€RD=> g = (4/3)Ï€GRD

Suppose,
Mass of earth is M, radius of earth is R.
Density of earth is, D = M/[(4/3)Ï€R³]
=> M = (4/3)Ï€R³D
Now, g = GM/R²
=> g = G Ã— (4/3)Ï€R³D Ã— (1/R²)
=> g = G Ã— (4/3)Ï€RD
=> g = (4/3)Ï€GRD