question_answer

Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:

A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limits\[-\phi \] and\[+\phi \]. For on angular displacement\[\theta (|\phi |<\phi ),\]the tension the string and the velocity of the bob ar T and respectively. The following relations hold good (1)\[T=mg\,\cos \theta =(M{{v}^{2}})/L\] (2)\[T\,\cos \theta =Mg\] (3) The   magnitude   of   the   tangential acceleration of the bob \[|{{a}_{T}}|=g\sin \theta \] (4) \[T=Mg\text{ }cos\theta \]

A)  1, 2 and 3 are correct

B)  1 and 2 are correct

C)   2 and 4 are correct

D)  1 and 3 are correct

Correct Answer: D

Solution :

                 From die figure it is clear that                 \[T-Mg\text{ }cos\theta =\]centripetal force                 \[T-Mg\text{ }cos\theta =\frac{M{{v}^{2}}}{L}\]                                 Also, tangential acceleration \[|{{a}_{T}}|=g\sin \theta \].