The speed with which the earth would have to rotate about its axis so that a person on the equator would weigh 3 5 th as much as at present is ( g = gravitational acceleration, R = equatorial radius of the earth.)

Step-by-step solution

The apparent acceleration due to gravity at the equator when the Earth rotates with angular speed is given by: g' = g - R ^2 The present weight of a person at the equator is approximately mg (neglecting the small effect of the Earth's current rotation). The new weight is given as 3 5 of the present weight. mg' = 3 5 mg g' = 3 5 g Substituting the expression for g' : g - R ^2 = 3 5 g R ^2 = g - 3 5 g R ^2 = 2 5 g ^2 = 2g 5R = 2g 5R Answer: 2g 5R