The diameters of two planets are in the ratio 4: 1 and their mean densities in the ratio 1: 2. The acceleration due to gravity on the planets will be in ratio

Question

The diameters of two planets are in the ratio 4: 1 and their mean densities in the ratio 1: 2. The acceleration due to gravity on the planets will be in ratio (A) 1: 2 (B) 2: 3 (C) 2: 1 (D) 4: 1

Tardigrade Admin · Accepted Answer

The gravity g=(4/3)Gπ Rρ The ratio of gravities on the planet (g1/g2)=(ρ 1R1/ρ 2R2) (g1/g2)=(1/2)× (4/1)=(2/1)

Q. The diameters of two planets are in the ratio 4 : 1 and their mean densities in the ratio 1 : 2. The acceleration due to gravity on the planets will be in ratio

1 : 2

2 : 3

2 : 1

4 : 1

The gravity $g = \frac{4}{3} G π Rρ$ The ratio of gravities on the planet $\frac{g _{1}}{g _{2}} = \frac{ρ _{1} R _{1}}{ρ _{2} R _{2}}$ $\frac{g _{1}}{g _{2}} = \frac{1}{2} \times \frac{4}{1} = \frac{2}{1}$

Q. The diameters of two planets are in the ratio 4 : 1 and their mean densities in the ratio 1 : 2. The acceleration due to gravity on the planets will be in ratio

1 : 2

2 : 3

2 : 1

4 : 1

The gravity g=34​GπRρ The ratio of gravities on the planet g2​g1​​=ρ2​R2​ρ1​R1​​ g2​g1​​=21​×14​=12​

The gravity $g = \frac{4}{3} G π Rρ$ The ratio of gravities on the planet $\frac{g _{1}}{g _{2}} = \frac{ρ _{1} R _{1}}{ρ _{2} R _{2}}$ $\frac{g _{1}}{g _{2}} = \frac{1}{2} \times \frac{4}{1} = \frac{2}{1}$