Gravitation NCERT Solutions Class 11 Physics - Solved Exercise Question 8.16

Question 8.16:

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?

Answer: 

Weight of a body of mass m at the Earth’s surface, W = mg = 250 N
Body of mass m is located at depth, d = (1/2)R_e
Where,
R_e = Radius of the Earth
Acceleration due to gravity at depth g (d) is given by the relation:
g' = (1 - (d / R_e)g
= [1 - (R_e / 2R_e) ]g  =  (1/2)g
Weight of the body at depth d,
W' = mg'
= m X (1/2)g  =  (1/2) mg  =  (1/2)W
= (1/2) X 250  =  125 N