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Two planets 'A' and 'B' have the same radius. $ρ_{1} and ρ_{2}$ are densities of the materials in the planets such that $ρ_{1} < ρ_{2}$ . If the accelerations due to gravity on the surfaces of the planets A and B are $g_{A} and g_{B}$ respectively, then

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g_{A} < g_{B}

g_{A} > g_{B}

given information is not sufficient

g_{A} = g_{B}

answer is B.

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Detailed Solution

Acceleration due to gravity is given as:
$g = \frac{GM}{R^{2}}$
$M a s s = V o l u m e \times D e n s i t y$
$V o l u m e = \frac{4}{3} {πR}^{3}$
Substituting the values, we get,

$g = G \frac{4}{3} π R ρ$

$g \propto ρ$

$w h e r e M_{A} = M_{B} & R_{A} = R_{B}$

Here $ρ$ is the average density of $ρ_{1} and ρ_{2}$ from the given fig $ρ_{A} > ρ_{B}$

$∴ g_{A} > g_{B}$

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