• # question_answer                 A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved?                                                                                                                                A)                 14 m/s B)                 3 m/s                     C)                 3.92 m/s           D)                 5 m/s

Key Idea: In a horizontal circle, tension in the string provides the necessary centripetal force. For a ball to move in horizontal circle, the ball should satisfied the condition:                 Tension in the string = Centripetal force $\Rightarrow {{T}_{\max }}=\frac{M{{v}^{2}}_{\max }}{R}$ $\Rightarrow {{v}_{\max }}=\sqrt{\frac{{{T}_{\max }}.R}{M}}....(i)$                 Making substitution, we obtain                 ${{v}_{\max }}=\sqrt{\frac{25\times 1.96}{0.25}}$                 $=\sqrt{196}$                 $=14\,m/s$                 Note:    In a vertical circle, the tension at the highest point in zero and at lowest pint is maximum.