how much quicker than present must the earth revolve on its axis to make bodies at the equator experience weightlessness?and what will be the duration of the day ?

The speed is given as

v = rω = 2πr/T

 

Thus, current speed of earth is

 

 

In order to feel weightless, the gravitational force should be equal to the centripetal force.

Therefore, the new speed is

 

 

Thus, the earth has to move 17 times faster than present speed.

 

For this new speed, the duration of the day will be