question_answer

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

A) mg                                         

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

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

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

Correct Answer: B

Solution :

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