Question

The acceleration due to gravity on the surface of the moon is one sixth that on the surface of earths and the diameter of the moon is one fourth of that of the earth .the ratio of the escape velocity on moon and earth will be

Answer 1

Answer:

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The escape velocity of an object is given by the equation v  e  

=$\sqrt{2GM/R}$

where G is the gravitational constant, M is the mass of the planet, and R is the distance you're at from the centre of the planet.

In this case, the acceleration due to gravity on the surface of the moon is one sixth that on the surface of earth's and the diameter of the moon is one fourth of that of earth.

Therefore, the escape velocity in the moon will be ve=$\sqrt{2\frac{1}{6} GM/\frac{1}{4} R}$

=$\frac{1}{\sqrt{24} }$$\sqrt{2GM/R}$

Hence, the ratio of escape velocity on moon and earth will be

=$\frac{1} \sqrt{24}$

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Answer 2

diammeter of Earth = d

diammeter of Moon =d/4

radius of moon = d/8

Acceleration of gravity on Earth = g

Acceleration of gravity on Moon = g/6

Escape velocity on earth , V_e = √(2gd/2)

Escape velocity on moon, V_m = √(2g/6 *d/8) = √(2gd/48)

V_m/V_e = √(2gd/48)/√(2gd/2)

= √2/48 = 0.204