question_answer

A simple pendulum of length L and mass (bob) M is oscillating in a plane about a vertical line between angular limits \[-\varphi \] and\[+\varphi \]. For an angular displacement\[\theta (|\theta |<\varphi )\], the tension in the string and the velocity of the bob are T and v respectively. The following relations hold good under the above conditions                                                               [IIT 1986; UPSEAT 1998]

A)            \[T\cos \theta =Mg\]

B)  \[T-Mg\cos \theta =\frac{M{{v}^{2}}}{L}\]

C)            The magnitude of the tangential acceleration of the bob \[|{{a}_{T}}|\,=g\sin \theta \]

D)            \[T=Mg\cos \theta \]

Correct Answer: B

Solution :

 From following figure it is clear that \[T-Mg\cos \theta =\]Centripetal force                    \[\Rightarrow \] \[T-Mg\cos \theta =\frac{M{{v}^{2}}}{L}\]