If two planets of radii R1 and R2 have densities d1 and d2 , then the ratio of their respective acceleration due to gravity is [Kerala CEE 2013]

We know that gravity, acceleration due to gravity, g=43πGRdHere, given densities be d1 and d2 and radii be R1 and R2,So, g1g2=43πGR1d143πGR2d2⇒g1g2=R1d1R2d2

If two planets of radii R1 and R2 have densities d1 and d2 , then the ratio of their respective acceleration due to gravity is [Kerala CEE 2013]

We know that gravity, acceleration due to gravity, g=43πGRdHere, given densities be d1 and d2 and radii be R1 and R2,So, g1g2=43πGR1d143πGR2d2⇒g1g2=R1d1R2d2

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If two planets of radii R₁ and R₂ have densities d₁ and d₂ , then the ratio of their respective acceleration due to gravity is [Kerala CEE 2013]

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

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

$R_{1}^{3} d_{1} : R_{2}^{3} d_{2}$

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

answer is A.

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Detailed Solution

We know that gravity, acceleration due to gravity, $g = \frac{4}{3} π G R d$

Here, given densities be d₁ and d₂ and radii be R₁ and R₂,

So, $\frac{g_{1}}{g_{2}} = \frac{\frac{4}{3} π G R_{1} d_{1}}{\frac{4}{3} π G R_{2} d_{2}} \Rightarrow \frac{g_{1}}{g_{2}} = \frac{R_{1} d_{1}}{R_{2} d_{2}}$