Question

the weight of the body placed at the equator is half that of the weightat the poles then the angular velocity of the earth is?
(a)$\sqrt{g/R}$
(b)$\sqrt{2g/R}$
(c)$\sqrt{g/2R}$
(d)$\sqrt{3g/2R}$

Answer 1

The effect of rotation of earth changes the gravity
F = mg - mw²RSinФ
according value of force given we can write
mg/2 = mg -mw²RSinФ
g/2 = g - w²R (eliminating m and since at equater Ф =π/2 .SinФ =1)
Now solving we get 
w=√g/2R = angular velocity
therefore option c is answer