Question

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 $CD$ and its centre $O$ at the centre of line joining $AB$ and $CD$ (see figure). It is given a light push so that it starts rolling with its centre $O$ moving parallel to $CD$ in the direction shown. As it moves, the roller will tend to :

• A. turn left.
• B. turn right.
• C. go straight.
• D. turn left and right alternately.

Answer 1

Answer: (C)

go straight.

Answer 2

If central line is at a distance $r$ from instantaneous axis of rotation, the $r$ is at lesser distance from point on left than on right. Since $v = r \omega$, the roller will turn to left.