A bob of mass m is suspended by a light string of length L. It is imparted a horizontal velocity v_(o) at the lowest point A such that it completes a semi-circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point, C. This is shown in Fig. 6.6. Obtain an expression for The ratio of the kinetic energies (K_(B)"/"K_(C )) at B and C. Comment on the nature of the trajectory of the bob after it reaches the point C.

A bob of mass m is suspended by a light string of length L. It is impa

1.	A bob of mass m is suspended by a light string of length L. It is imparted a horizontal velocity v_(o) at the lowest point A such that it completes a semi-circular trajectory in the vertical plane with the string becoming slack only on reaching the topmost point, C. This is shown in Fig. 6.6. Obtain an expression for The ratio of the kinetic energies (K_(B)"/"K_(C )) at B and C. Comment on the nature of the trajectory of the bob after it reaches the point C.
Answer» Solution :The ratio of the kinetic energies at B and C is : `(K_B)/(K_C)=((1)/(2)mv_(B)^(2))/((1)/(2)mv_(c )^(2))=(3)/(1)` At point C, the string becomes slack and the velocity of the BOB is horizontal and to the left. It the connecting string is cut at this instant, the bob will execute a projectile motion with horizontal projection akin to a rock kicked HORIZONTALLY from the edge of a cliff. OTHERWISE the bob will continue on its circular PATH and complete the revolution.