A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically (see figure), with its axis perpendicular to and its centre at the centre of line joining and  (see figure). It is given a light push so that it starts rolling  with its centre moving parallel to in the direction shown. As it moves, the roller will send to :

If the centre line is r units away from the instantaneous axis of rotation,

we know $\mathrm{v}=\mathrm{r\omega }$ is the velocity of the point on the wheel which is in contact with the rail. 

The value of r will be more on the side of CD and less on the side of AB. Since, the radius of the wheel reduces along AB as it advances forward. Thus for an equal number of rotations it travels less along AB and turns left.

Hence the correct answer is turns left.