Login/Sign Up
Home » Assuming the earth to be a sphere of uniform mass density, how much would a body weigh halfway down to the centre of the earth if it weighed on the surface?
Assuming the earth to be a sphere of uniform mass density, how much would a body weigh halfway down to the centre of the earth if it weighed 250 \mathrm{~N} on the surface?
CBSE | Class 11 | Gravitation | NCERT | Physics
Assuming the earth to be a sphere of uniform mass density, how much would a body weigh halfway down to the centre of the earth if it weighed 250 \mathrm{~N} on the surface?

Weight of a body on the Earth’s surface is given as W=m g=250 \mathrm{~N}

Let R_{e} be the radius of the earth

Let d be at a distance halfway to the centre of the earth, then, d=R_{e} / 2

Acceleration due to gravity at d is given by the relation,

g_{\mathrm{d}}=\left(1-\mathrm{d} / \mathrm{R}_{e}\right) \mathrm{g}

g_{d}=\left(1-R_{e} / 2 R_{e}\right) g

=\mathrm{g} / 2

So, weight of the body at depth d will be given as

W^{\prime}=m g_{d}

=m g / 2=W / 2=250 / 2

=125 \mathrm{~N}

i

More Material