Gravitation

Question : 16 of 25

Marks: +1, -0

Assuming the earth to be a sphere of uniform mass density, how much would a body weigh half way down to the centre of the earth if it weighed 250 N on the surface?

Solution:

Variation of acceleration due to gravity g with depth d is

g'=g\left(1-\frac{d}{R}\right)

Weight of body at a depth d

m g'=m g\left(1-\frac{d}{R}\right)

=250\left(1-\frac{\frac{R}{2}}{R}\right)

=125 N.

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