Question

The escape velocity of a body from earth is about 11.2 km/s. Assuming the mass and radius of the earth to be about 81 and 4 times the mass and radius of the moon, the escape velocity in km/s from the surface of the moon will be

Answer 1

The escape velocity of the moon is Ve (moon) =  2.488 Km/s

Explanation:

Escape velocity =  √ 2GM /R

Ve (earth) / Ve (moon) =  √ M (earth) / M (moon) x R (earth) / R (moon)

Ve (earth) / Ve (moon) =  √ 81 /M x R / 4R

Ve (earth) / Ve (moon) =  √ 81/4 = 9/2

Ve (moon) = 2/9 Ve (earth)

Ve (moon) =  2/9  x 11.2

Ve (moon) =  2.488 Km/s

Hence the escape velocity of the moon is Ve (moon) =  2.488 Km/s

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The escape velocity on the moon is less than that on the earth. State with reasons whether the sentence are true or false. ?

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Answer 2

Hey Jayanth! Thanks for putting your doubt.

Given :-

• the escape velocity of the earth = 11.2 km/s
• mass of earth = 81 × mass of moon
• radius of earth = 4 × radius of moon

To find :-

• the value escape velocity on moon

Solution :-

We know by formula and applying it in the question we have :

Ve/ Vm = √2 GMe/ Re / √2 GMm/ Rm

Ve/ Vm = √1/ Re / √1/ Rm

Ve/ Vm = √ 81 Mm/ 4 Rm × √ Rm / √Mm

Ve/ Vm = √81/ 4

Ve/ Vm = 9/2

11.2 / Vm = 9/2

11.2/ Vm = 4.5

Vm = 11.2 / 4.5

Vm = 2.48 Km/s

Hence, the escape velocity on the moon is 2.48 Km/s.