The rotation of the earth 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. `pi sqrt((R)/(g))`
B. `(pi)/(2)sqrt((R)/(g))`
C. `(pi)/(3)sqrt((R)/(g))`
D. `pi sqrt((g)/(R))`

Answer

A

Explanation

`0=g-Romega^(2)cos^(2) 60^(@)`
or `omega^(2)=(4g)/(R)or omega=2sqrt((g)/(R))`
`(2pi)/(T)=2sqrt((g)/(R))rArrT=pisqrt((R)/(g))`