question_answer

A simple pendulum of length L swings in a vertical plane. The tension of the string when it makes an angle \[\theta \] with the vertical and the bob of mass m moves with a speed v is (g is the gravitational acceleration)

A)  \[m{{v}^{2}}/L\]

B)  \[mg\,\cos \theta +m{{v}^{2}}/L\]

C)  \[mg\,\cos \theta \,-m{{v}^{2}}/L\]

D)  \[mg\,\cos \theta \]

Correct Answer: B

Solution :

 The situation is given below . For motion along a vertical circular track, the required centripetal force is along the radius and towards the centre of the circle is given by \[T-mg\,\cos \theta =\frac{m{{v}^{2}}}{L}\] \[\Rightarrow \] \[T=\frac{m{{v}^{2}}}{L}+mg\cos \theta \]