question_answer

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

A) \[16\,\,ml\]                       

B) \[6\,\,ml\]

C) \[5\,\,ml\]                                          

D)  \[3\,\,ml\]

Correct Answer: A

Solution :

                \[T\sin \theta =\frac{m{{v}^{2}}}{r}\]                                      ...(i)                 \[T\cos \theta =mg\]                 \[v=r\,\,\omega \]and\[\sin \theta =\frac{r}{l}\] Putting these values in Eq (i), we get                 \[T\times \frac{r}{l}=m{{\omega }^{2}}r\]                 \[T=m{{\omega }^{2}}l\]                 \[T=m{{(2\pi n)}^{2}}l\]                 \[T=m{{\left( 2\pi \times \frac{2}{\pi } \right)}^{2}}l\]                 \[T=16\,\,ml\]