With what angular velocity the earth should spin in order that a body lying at `37^@` latitude may become weightless.

Options

A. `(5)/(4) sqrt((g)/(R))`
B. `(25)/(16) sqrt((g)/(R))`
C. `(5)/(3)sqrt((g)/(R))`
D. `(25)/(g) sqrt((g)/(R)`

Answer

A

Explanation

We have
`mg'=mg -m omega_(2) R cos_(2) alpha`
for weightless Net
`0=mg - m omega_(2) R cos_(2) theta`
`rArr omega = sqrt((g)/(R)) xx(1)/(cos theta)`

`=sqrt((g)/(R))(1)/(4//5)=(5)/(4) sqrt((g)/(R))`