What is the ratio of the escape velocity of the Earth to orbital velocity on the Earth?

$\sqrt{2}$

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$\sqrt{3}$

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Solution

The correct option is A
$\sqrt{2}$

Step 1: Given data: Escape velocity on the earth is given as $V_{e} = \sqrt{2 g R}$ where, g = acceleration due to gravity, R = radius of earth
Orbital velocity for the earth is given as $V_{o} = \sqrt{g R}$
Step 2: Calculation
Ratio = $\frac{V_{e}}{V_{o}} = \frac{\sqrt{2 g R}}{\sqrt{g R}} = \sqrt{2}$
Therefore the ratio is $\sqrt{2}$
Hence the correct option is (A) .

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What is the ratio of the escape velocity of the Earth to orbital velocity on the Earth?

The correct option is A 2Step 1: Given data: Escape velocity on the earth is given as Ve=2gR where, g = acceleration due to gravity, R = radius of earthOrbital velocity for the earth is given as Vo=gRStep 2: Calculation Ratio = VeVo=2gRgR=2Therefore the ratio is 2Hence the correct option is (A) .