What should be the angular velocity of earth due to rotation about its own axis so that the weight at equator becomes ( 3 5 )^ th of initial value? ( g = acceleration due to gravity, R = radius of earth)

Step-by-step solution

The effective acceleration due to gravity at the equator due to the rotation of the Earth is given by: g' = g - ^2 R The weight of a body at the equator is: W' = mg' = m(g - ^2 R) According to the given condition, the new weight becomes 3 5 of the initial weight ( mg ). m(g - ^2 R) = 3 5 mg g - ^2 R = 3 5 g ^2 R = g - 3 5 g ^2 R = 2 5 g ^2 = 2g 5R = ( 2g 5R )^ 1 2 Answer: ( 2g 5R )^ 1 2