The rotation of the earth having radius R about its axis speeds up to a value such that a man at latitude angle `60^(@)` feels weightlessness. The duration of the day in such a case is

Options

A. `8pisqrt((R)/(g))`
B. `8pisqrt((g)/(R))`
C. `pisqrt((R)/(g))`
D. `4pisqrt((g)/(R))`

Answer

C

Explanation

`g'=g-omega^(2)cos60`
`g'=g-omega^(2)Rcos^(2)60`
`g'=0,g=omega^(2)Rcos^(2)60`
`sqrt((4g)/(R))=omega,t=(2pi)/(omega)=2pisqrt((R)/(4g))=pisqrt((R)/(g))`