The angular velocity of the earth with which it has to rotate so that the acceleration due to gravity on `60^@` latitude becomes zero is

Options

A. `2. 5 xx 10^(-3)` rad/s
B. `5.0 xx 10^(-1)`rad/s
C. `10 xx 10^(1)` rad/s
D. `7.8 xx 10^(-2)` rad/s

Answer

A

Explanation

g. = g - `omega^(2) R cos^(2) lambda rArr 0 = g - omega^(2) R cos^(2) 60^(@)`
`0 = g - (omega^(2)R)/(4) rArr omega = 2 sqrt((g)/(R)) = (1)/(400) ("rad")/("sec")`
= 2.5 `xx 10^(-3) ("rad")/("sec")`