question_answer

    A simple pendulum with length L and mass of the bob is vibrating with an amplitude a. Then the maximum tension in the string is

A)  \[mg\]                                

B)  \[mg\left[ 1{{\left( \frac{a}{1} \right)}^{2}} \right]\]

C)  \[mg{{\left[ 1+\frac{a}{2L} \right]}^{2}}\]            

D)  \[mg{{\left[ 1+\left( \frac{a}{L} \right) \right]}^{2}}\]

Correct Answer: B

Solution :

                \[T-mg\cos \theta =\frac{m{{v}^{2}}}{L}\] T is maximum, when\[\theta =0\] \[\therefore \]  \[{{T}_{\max }}=mg+\frac{mv_{\max }^{2}}{L}\]                 \[=mg+\frac{m{{a}^{2}}{{\omega }^{2}}}{L}\]                 \[=mg\left[ 1+{{\left( \frac{a}{L} \right)}^{2}} \right]\]