question_answer

A uniform rod of length \[l\]and mass M is suspended on two vertical inextensible string as shown in the figure. Calculate tension T in left string at the instant, when right string snaps.  

A)  \[mg/2\]          

B)  \[mg\]

C)  \[mg/4\]          

D)  \[mg/8\]

Correct Answer: C

Solution :

 Let the tension in the string be T and the acceleration of the centre of mass of the rod downwards be a. Then, \[mg-T=ma\] Again, \[\frac{mgl}{2}=I\,\,\alpha =\frac{m{{l}^{2}}}{3}\times \frac{a}{l/2}\] \[\Rightarrow \]            \[a=\frac{3}{4}g\] \[\therefore \]    \[T=\frac{mg}{4}\]