Question

a body a weight of 100N on the surface of the earth.what will be its weight when it is taken to the centre of the earth?
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Answer 1

Explanation:

For distance between object and centre of the earth we have

Acceleration due to gravity at height be gh = (R/R + h)2

mg1 = GMm / (R + h)2

gh = GM/(R + h) 2

Now gh/g = R^2/(R + h) 2

or gh = g(R/R + h) 2

given h = R/2

gh = g(R/R+R/2) 2

gh = g(2R / 3R) 2

= g x 4/9

Acceleration due to gravity at depth = R/2

gD = g(1 - D/R)

gD = g(1 - R/2/R)

= g/2

Wh / WD = gh /gD

= 4g/9 / g/2

= 4g/9 x 2/g = 8/9