Question

A stone weighs 100 N on the surface of the earth. the ratio of its weight at aheight of half the radius of the earth to its weight at a depth of half the radius of the earth will be approximately

Answer 1

Answer:

Acceleration due to gravity at height h= R/2

Therefore, gh= (R/R+h)2 = g(R/R +R/2)2 = g(R/3R/2)2 = 4g/9

Acceleration due to gravity at depth d= R/2

Therefore, gd= g(1-d/R) = g (1- ((R/2)/R) = g/2

Let’s calculate the ratio of the weight:

Wh/Wd= mgh/mgd

By simplifying we get, gh/gd

By putting the values we get, (4g/9)/(g/2)

On simplifying we get, 8/9= 0.9. This would be the approximate value.