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 ?

Assuming the earth to be a sphere of uniform mass density, how much wo

1.	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» <html><body><p></p>Solution :`<a href="https://interviewquestions.tuteehub.com/tag/implies-1037962" style="font-weight:bold;" target="_blank" title="Click to know more about IMPLIES">IMPLIES</a>` Suppose, <a href="https://interviewquestions.tuteehub.com/tag/g-1003017" style="font-weight:bold;" target="_blank" title="Click to know more about G">G</a> and `g_d`are the acceleration <a href="https://interviewquestions.tuteehub.com/tag/due-433472" style="font-weight:bold;" target="_blank" title="Click to know more about DUE">DUE</a> to gravity at the surface and at the depth d of earth respectively and `W and W_d` are the weights of body at the surface and at the depth of earth respectively.<br/> `g(d) = g(1-d/<a href="https://interviewquestions.tuteehub.com/tag/r-611811" style="font-weight:bold;" target="_blank" title="Click to know more about R">R</a>)` <br/> `:. g(d) = g (1-(R/2)/R)""[ :. d = R/2]` <br/> `= g (1-1/2)` <br/> `=g/2` <br/> `:.`Weight of body of mass m at depth d <br/> W(d) = mg (d) <br/> `=(mg)/2 ""[ :. g(d) =g/2]` <br/> `W(d) = W/2 ""[ :. mg = W]`<br/> `:. W(d) = (<a href="https://interviewquestions.tuteehub.com/tag/250-297421" style="font-weight:bold;" target="_blank" title="Click to know more about 250">250</a>)/2` <br/> `:. W(d) = 125 N`</body></html>