In order to make the effective acceleration due to gravity at the equator to zero, the numerical value of the angular velocity of rotation of the earth should be
[Radius of the earth=6400 km, `g=10m/s^(2)`]

Options

A. zero
B. `(1)/(800) ` rad `sec^(-1)`
C. `(1)/(80) "rad" sec^(-1)`
D. `(1)/(8) "rad " sec^(-1)`

Answer

B

Explanation

g. = g - `omega^(2) R cos^(2) lambda`
To makes effective acceleration due to gravity zero at equator `lambda` = 0 and g. = 0
`therefore 0 = g - omega^(2) R rArr omega = sqrt((g)/(R)) = (1)/(800) ("rad")/(s)`