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? | Learn NCERT solution | Education portal Class 11 Physics | Study online Unit-8 Gravitation



Q.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)Re
Where,
Re = Radius of the Earth
Acceleration due to gravity at depth g (d) is given by the relation:
g‘ = (1 – (d / Re)g
= [1 – (Re / 2Re) ]g  =  (1/2)g
Weight of the body at depth d,
W‘ = mg
= m × (1/2)g  =  (1/2) mg  =  (1/2)W
= (1/2) × 250  =  125 N