question_answer

                                              A stone is attached to one end of a string and rotated in a vertical circle. If string breaks at the position of maximum tension, it will break at:                                                                                                           

A)                 A          

B)                 B            

C)                 C          

D)                 D

Correct Answer: B

Solution :

                                When string makes an angle \[\theta \] with the vertical in a vertical circle, then                 \[T-mg\cos \theta =\frac{m{{v}^{2}}}{l}\]                 or            \[T=mg\cos \theta +\frac{m{{v}^{2}}}{l}\]                 Tension is maximum when cos \[\theta \] = + 1 i.e.,                 \[\theta \] = 0.                 Thus, \[\theta \] is zero at lowest point B. At this point tension is maximum. So, string will break at point B.                 Note:    The critical speed of a body n circular path \[{{v}_{c}}=\sqrt{Rg},\,R\]=radius of path.                 If at the highest point the speed is less than this the string would become slack and the body would leave the circular path.