(a) At what rate should the earth so that the apparent `g` at the equator becomes zero? What will be the length of the day in this situation?
(b) A body stretches a spring by a particular length at the earth's surface at equator. At what height above the south pole will it stertch the same spring by the same length? Assume the earth to be spherical.

Explanation

(a) `g'=g-omega^(2)R_(e )`
`g'=0`
`0=g-omega^(2)R_(e)`
`omega=sqrt(g/(R_(e)))=1.237xx10^(-3) rad//s`
`T=(2pi)/(omega)=2pisqrt((R_(e))/g)=84.6 mi n` or `1.4 hr`
(b) `kx=mg'_("equator")=mg"`
`g'_("equator")=g"`
`g-omega^(2)R_(e)=g/((1-h/(R_(e)))^(2))=g(1-(2h)/(R_(e)))`
Assuming `h lt lt R_(e)`
`omega^(2)R_(e)=(2h)/(R_(e))`
`h=(omega^(2)R_(e)^(2))/2=((2pi)/(24xx3600))^(2)xx((6400xx10)^(2))/2`
`=10819 =10.8 km`