Question

The diameters of two planets are in the ratio of 4 : 1 & mean density have ratio 1 : 2, then the ratio of g on the planets will be –

• A. 1 : 2
• B. 1 : 4
• C. 2 : 1
• D. 4 : 1

Answer 1

Answer: (C)

2 : 1

Answer 2

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

given R₁ : R₂ = 4 : 1 & r₁ : r₂ = 1 : 2

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