Question

If the mass of earth is doubled and radius is halved what will be accelaration due to gravity

Answer 1

We know that, g = 9.8 m/s²

Let, find out the ratio first

M = 2M

Gravitational Constant = G

R = R/2

Ratio =A.T.Q / Original g

Ratio = G2M/(R²/4) / GM/(R²)

Ratio = 8GM/R² / GM/R²

Ratio = 8GM × R² / R² × GM

Ratio = 8:1

So, According to the question , g will be 8 × 9.8 , Which equals 78.4 m/s²

Answer 2

We know that, gravitational acceleration, g= GM/R² (where M is the mass of the earth)

If mass of the earth is doubled and radius of earth is halved then the new gravitational acceleration is

g'= G(2M)/(R/2)²= 8[GM/R²]= 8g

Hence the acceleration due to gravity will be increased by 8 times of initial  value