Question

A rod of mass m and length L, lying horizontally, is free to rotate about a vertical axis through its centre. A horizontal force of constant magnitude F acts on the rod at a distance of L/4 from the centre. The force is always perpendicular to the rod. Find the angle rotated by the rod during the time t after the motion starts

Answer 1

A rod of mass m and length L, lying horizontally, is free to rotate about a vertical axis passing through its centre.
A force F is acting perpendicular to the rod at a distance L/4 from the centre.
Therefore torque about the centre due to this force
i _i = F × r = FL/4.
This torque will produce an angular acceleration α.