Question

The radius of the moon is one-fourth and it's mass is one eighty-first that of the earth. If the acceleration due to gravity on the surface of the earth is 9.8m/s^2,what is it's value on the moon's surface

Answer 1

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Answer 2

Answer:      1. 9 6 m/s^2

Explanation:

Let g(e) be acceleration due to gravity on Earth

Then by Newton’s Law of Gravitation

g(e) = ( G . M(e) ) / R(e)^2

where M(e) and R(e) are mass and Radius of the Earth and G is the Universal Constant of Gravitation.

The acceleration due to gravity on Moon can be written as

g(m) = ( G . M(m) ) / R(m)^2

where M(m) and R(m) are mass and Radius of the Moon.

We are given that M(m) = M(e)/80 and R(m) = R(e)/4

g(m) = { G . (M(e)/80 ) } / {R(e)/4}^2 = { (G.M(e) ) /(R(e))^2 }. (16/80)

g(m) = g(e) /5 = (9.8 /5) m/s^2 = 1. 9 6 m/s^2