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

Options

A. (a)`8pisqrt((R)/(g))`
B. (b)`8pisqrt((g)/(R))`
C. (c)`pisqrt((R)/(g))`
D. (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))`