First slide

Gravitational field intensity

Question

Two planets have radii R₁ and R₂ and densities d₁ and d₂respectively. The ratio of the acceleration due to gravity on them will be :

Easy

A

R₁d₂: R₂d₁
B

R₁d₁: R₂d₂
C

$R_{1}^{2} d_{1} : R_{2}^{2} d_{2}$
D

$R_{1} d_{1}^{2} : R_{2} d_{2}^{2}$

Solution

$g = \frac{GM}{R^{2}} = \frac{Gd (\frac{4}{3} {πR}^{3})}{R^{2}} = \frac{4 πGdR}{3} \Rightarrow \frac{g_{1}}{g_{2}} = \frac{d_{1} R_{1}}{d_{2} R_{2}}$

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