Question

The radii of two planets are respectively R₁& R₂ and their densities are respectively r₁&r₂. The ratio of the acceleration due to gravity at their surface is –

• A. g₁ : g₂ = : $\frac { \rho _ { 2 } } { \mathrm { R } _ { 2 } ^ { 2 } }$
• B. g₁ : g₂ = R₁R₂ : r₁r₂
• C. g₁ : g₂ = R₁r₂ : R₂r₁
• D. g₁ : g₂ = R₁r₁ : R₂, r₂

Answer 1

Answer: (D)

g₁ : g₂ = R₁r₁ : R₂, r₂

Answer 2

The value of g at surface

g = $\frac { 4 } { 3 } \pi \mathrm { GR } \rho$

so, $\frac { \mathrm { g } _ { 1 } } { \mathrm {~g} _ { 2 } }$ = $\frac { \frac { 4 } { 3 } \pi \mathrm { GR } _ { 1 } \rho _ { 1 } } { \frac { 4 } { 3 } \pi \mathrm { GR } _ { 2 } \rho _ { 2 } }$ ̃ $\frac { \mathrm { g } _ { 1 } } { \mathrm {~g} _ { 2 } }$ =