If earth is supposed to be a sphere of radius R , if `g_(30)` is value of acceleration due to gravity at latitude of `30^(@)` and g at the equator, the value of `g-g_(30^(@))` is

Options

A. `(1)/(4) omega^(2) ` R
B. `(3)/(4) omega^(2) `R
C. `omega^(2)` R
D. `(1)/(2) omega^(2)` R

Answer

B

Explanation

Acceleration due to gravity at lattitude .`lambda`. is given by
` g_(lambda) = g_(e) - R_(e) omega^(2) cos^(2) lambda`
At equator , `lambda = 90^(@) rArr cos lambda = cos 90^(@) = 0 `
or `g_(lambda) = g_(e) = g ` (as given in question )
At `30^(@) , g_(30) = g - R omega^(2) cos^(2) 30 = g - (3)/(4) R omega^(2)`
or , g - `g_(30) = (3)/(4) R omega^(2)`