Solve the integral I=∫R∞GMmx2dx
- GMm ln(R)
This expression represents the gravitational potential energy which is obtained by integrating GMm/x2 between the limits infinity (∞) and radius of the earth (R).
Consider a particle of mass m suspended vertically by a string at the equator. Let R and M denote the radius and the mass of the earth respectively. If ω is the angular velocity of earth's rotation about its own axis, the tension in the string is equal to