The ratio of the radii of the planets $P_{1}$ and $P_{2}$ is $k_{1} .$ The corresponding ratio of the acceleration due to the gravity on them is $k_{2} .$ The ratio of the escape velocities from them will be

k_{1} k_{2}

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\sqrt{k_{1} k_{2}}

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\sqrt{(k_{1} / k_{2})}

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\sqrt{(k_{2} / k_{1})}

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Solution

The correct option is C $\sqrt{k_{1} k_{2}}$
$v_{e} = \sqrt{2 g R}$
$∴ \frac{(v_{e}) p_{1}}{(v_{e}) p_{2}} = \frac{\sqrt{g_{1} R_{1}}}{\sqrt{g_{2} R_{2}}} = \sqrt{{(\frac{g_{1}}{g_{2}}) \times (\frac{R_{1}}{R^{2}})}} = \sqrt{k_{1} k_{2}}$

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The ratio of the radii of the planets P1 and P2 is k1. The corresponding ratio of the acceleration due to the gravity on them is k2. The ratio of the escape velocities from them will be

The correct option is C √k1k2ve=√2gR∴(ve)p1(ve)p2=√g1R1√g2R2=√{(g1g2)×(R1R2)}=√k1k2

The ratio of the radii of the planets $P_{1}$ and $P_{2}$ is $k_{1} .$ The corresponding ratio of the acceleration due to the gravity on them is $k_{2} .$ The ratio of the escape velocities from them will be

The correct option is C $\sqrt{k_{1} k_{2}}$
$v_{e} = \sqrt{2 g R}$
$∴ \frac{(v_{e}) p_{1}}{(v_{e}) p_{2}} = \frac{\sqrt{g_{1} R_{1}}}{\sqrt{g_{2} R_{2}}} = \sqrt{{(\frac{g_{1}}{g_{2}}) \times (\frac{R_{1}}{R^{2}})}} = \sqrt{k_{1} k_{2}}$