The bob of mass m of a resting pendulum is given a sharp hit, imparting a horizontal velocity of 10 ,gl , where l represents the pendulum's length. Determine the tension in the string when the bob is at its highest point.

Step-by-step solution

Let u be the velocity at the lowest point and v be the velocity at the highest point. Using conservation of mechanical energy between the lowest and highest points: 1 2 mu^2 = 1 2 mv^2 + mg(2l) Given u = 10gl , substituting this yields: 1 2 m(10gl) = 1 2 mv^2 + 2mgl 5mgl = 1 2 mv^2 + 2mgl 1 2 mv^2 = 3mgl v^2 = 6gl At the highest point, both tension T and weight mg act downwards towards the center of the circular path. The equation for centripetal force is: T + mg = mv^2 l Substituting v^2 = 6gl : T + mg = m(6gl) l