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: [AIPMT 2000]

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.