Assuming the earth to be a sphere of uniform mass density

cbse
gravitation

#1

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


#2

Weight of the body at the earth’s surface
w = mg = 250 N … (i)
Acceleration due to gravity at depth h from the earths surface
g’ = g(1-h/R)
Here, h= R/2
g’ = g(1-R/2/R) = g(1-1/2)
g’ = g/2
Weight of the body at depth h

w’ = mg = mg/2

Using Eq.(i), we get w’ = 250/2 = 125N
Weight of the body will be 125 N