Question

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

• A. 3.6
• B. 2.2
• C. 1.8
• D. None of these

Answer 1

The correct option is D None of these

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