A thin rod MN , free to rotate in the vertical plane about the fixed end N , is held horizontal. When the end M is released the speed of this end, when the rod makes an angle with the horizontal, will be proportional to: (see figure)

Step-by-step solution

When the rod makes an angle aligned & Displacement of centre of mass = l 2 &m g l 2 = l 2 I ^2 &m g l 2 = m l^2 6 ^2 ( M.I. of thin aligned uniform rod about an axis passing through its centre of mass and perpendicular to the aligned & . rod I= m l^2 12 ) & = 3 g l aligned Speed of end = l= 3 g l i.e., Speed of end,