If bodies at a latitude of 45^@of the earth are to be weightless, what should be earth.s time period of rotation?

If bodies at a latitude of 45^@of the earth are to be weightless, what

1.	If bodies at a latitude of 45^@of the earth are to be weightless, what should be earth.s time period of rotation?
Answer» Solution : The acceleration due to gravity at latitude `phi`is `g_phi =g - R omega^2 cos^2 phi` For bodies to be WEIGHTLESS at a latitude of`45^@` then “ `g_phi` ” must be zero. ` rArr 0 = g - R omega^2 cos^2 45^@ rArr 0 = g - R omega^(2) 1/2 rArr R omega^2 = 2g rArr omega = sqrt((2g)/(R ))` We KNOW that , `omega = (2PI)/(T) rArr (2pi)/(T) = sqrt((2g)/(R ))rArr T = 2pi sqrt((R)/(2g)) " or " T = pi sqrt((2R)/(g))`