The rotation of the Earth (of radius R ) about its axis speeds up to a value such that a man at latitude angle 45^ feels weightlessness. The duration of a day in such a case is

Step-by-step solution

Given that, angle of latitude, =45^ We know that, the expression of gravity at latitude angle is g_ =g- ^2 R ^2 The weight of man of mass m at this point w=m g_ =m (g- ^2 R ^2 45^ ) According to question, man feels weightlessness aligned w & =0 m (g- ^2 R ^2 45^ ) & =0 aligned But m 0 , then g- ^2 R ^2 45^ =0 = 2 g R Now, using time period, (duration of day) =T= 2 =2 R 2 g = 2 R g