A solid cylinder of mass \(50\) kg and radius \(0.5\) m is free to rotate about the horizontal axis. A massless string is wound around the cylinder with one end attached to it and the other end hanging freely. The tension in the string required to produce an angular acceleration of \(2\) revolutions/s² will be:
1. \(25\) N
2. \(50\) N
3. \(78.5\) N
4. \(157\) N

A uniform rod \(AB\) of length \(l\) and mass \(m\) is free to rotate about point \(A\). The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about \(A\) is \(\dfrac{ml^2}{3}\) the initial angular acceleration of the rod will be: 
       
1. \(\dfrac{2g}{3l}\)
2. \(\dfrac{mgl}{2}\)
3. \(\dfrac{3}{2}gl\)
4. \(\dfrac{3g}{2l}\)