Question

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? Question 8.16 gravitation

Answer 1

We know,
accⁿ due to gravity at depth h from earth's surface ,
g = go( 1 - h/r)
here, h = r/2

g = go(1 - r/2r) = go/2

Now, weight of body at the surface of the earth = 250N = mgo

hence, weight of body at depth R/2 = mgo/2 = 250/2 = 125 N

Answer 2

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