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. |
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