Question

Mass m tube Earth density fE Earth mass ME Earth radius RE The tabe pass the center of the earth Eind a) angalar velocity at distancel) fro m the center h) find movement fanction of the mass any c) find force thot act to the mass at any distance U) tron cehter

Answer 1

We need to find gravitational field on a point at a distance r from the center

So, we consider a spherical shell at a distance r from the center of mass dM

Now,

GdM dE = 2

МЕ 4/3т РЕ * 4тр?dr Е dM =

Now integrating the gravitational field and r we get

GMET E = 3

Now, force at the point mass m at a point r

GMEmr F =

GMEтr та РЗ

GMET dv dt

GMET du dr

GMET - dr vdu =

Initially taking velocity as zero at r =R

Finally velocity as v and r=l

We get

GME(R212) = R3

Angular velocity is zero as there is no movement perpendicular to the center of the earth