A) \[\theta ={{\cos }^{-1}}\left( \frac{1}{3} \right)\]
B) \[\theta ={{\cos }^{-1}}\left( \frac{2}{3} \right)\]
C) \[\theta ={{60}^{0}}\]
D) \[\theta =\,zero\]
E) None of these
Correct Answer: B
Solution :
By law of conservation of energy, loss in PE = gain in KE \[\Rightarrow \] \[mgl(1-\cos \theta )=\frac{1}{2}m{{v}^{2}}\] \[\Rightarrow \] \[\frac{m{{v}^{2}}}{l}=2mg\,(1-\cos \theta )\] At point of breaking, \[mg\cos \theta =\frac{m{{v}^{2}}}{l}\] \[\therefore \] \[mg\cos \theta =2mg\,(1-\cos \theta )\] \[\Rightarrow \] \[\cos \theta =\frac{2}{3}\] \[\Rightarrow \] \[\theta ={{\cos }^{-1}}\left( \frac{2}{3} \right)\]You need to login to perform this action.
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