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CMC Medical CMC-Medical VELLORE Solved Paper-2010

  • question_answer
    In a simple pendulum, the breaking strength of the string is doubled the weight of the bob. The bob is released from rest when the string is horizontal. The string breaks when it makes an angle \[\theta \] with the vertical

    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, \[mg\cos \theta =\frac{m{{v}^{2}}}{l}\] \[\therefore \]  \[mg\cos \theta =2mg\,(1-\cos \theta )\] \[\Rightarrow \]               \[\cos \theta =\frac{2}{3}\] \[\Rightarrow \]               \[\theta ={{\cos }^{-1}}\left( \frac{2}{3} \right)\]


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