question_answer

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

A)  \[2mk{{r}^{2}}t\]                                            

B)  \[mk{{r}^{2}}{{t}^{2}}\]

C)  \[m{{k}^{2}}{{r}^{2}}t\]               

D)  \[m{{k}^{2}}r{{t}^{2}}\]

Correct Answer: B

Solution :

                Tension in the string \[T-mg\cos \theta =\frac{m{{v}^{2}}}{L}\] T is maximum, when \[\theta ={{0}^{o}}\]                 \[\therefore \]   \[{{T}_{\max }}=mg+\frac{m{{v}^{2}}_{\max }}{L}=mg+\frac{m{{a}^{2}}{{\omega }^{2}}}{L}\] \[\because \]     a is amplitude                 \[{{T}_{\max }}=mg+\frac{m{{a}^{2}}}{L}\times \frac{g}{L}\]                 \[=mg\left[ 1+{{\left( \frac{a}{L} \right)}^{2}} \right]\]