question_answer

A string of length I fixed at one end carries a mass m at the other end. The string makes \[\frac{2}{\pi }\,rev/s\] around the horizontal axis through the fixed end as shown in the figure, the tension in the string is    

A)  16 ml              

B)  4 ml                                                  

C)  8 ml                            

D)  2 ml  

Correct Answer: A

Solution :

By diagram \[T\,cos\,\theta \,\,=\,\,mg\]                                              ... (i) \[T\,\sin \,\theta \,\,=\,\,\frac{m{{v}^{2}}}{r}\] \[\Rightarrow \,\,\,\,\,\,\,\,\operatorname{v} =\omega r\,\,\,\Rightarrow \,\,\,T \times \,\,\frac{r}{l}\,\,=\,\,m{{\omega }^{2}}r\] \[\Rightarrow \,\,\,~\,\,\,\,\,T=m{{\omega }^{2}}l\]          \[\left( \because \,\,\,\,\,\sin \,\,\theta \,\,=\,\,\frac{r}{l} \right)\] \[=\,\,\,\,m{{\left( 2\pi \times \frac{2}{\pi } \right)}^{2}}l\] \[\operatorname{T}\,\,=\,\,16\,ml\]