A particle attached to a string of length r is moving on vertical circular path continuously. If the speed of the particle at the highest point is 7 gr , then the ratio of the respective tension in the string holding it at the highest and the lowest points is ( g = acceleration due to gravity)

Step-by-step solution

The given situation is shown in the figure At highest point A , v_A= 7 g r T_d and T_s are tensions in the string when particle is at highest position (A) and lowest position (B) . At point A . aligned & m v_A^2 r =T_A+m g & m( 7 g r )^2 r =T_A+m g & 7 m g=T_A+m g & T_A=6 mg & aligned At point B by the law of conservation of energy, change in potential energy = Change in kinetic energy aligned & m g(2 r)= 1 2 m v_ B ^2- 1 2 m v_A^2 & 2 m g r= 1 2 m v_B^2- 1 2 m(7 g r) & 4 g r=v_B^2-7 g r & v_s= 11 g r aligned At lo