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Question

A roller is made by joining together two cones at their vertices $0$. It is kept on two rails $AB$ and $CD$, which are placed asymmetrically (see figure), with its axis perpendicular to $CD$ and its center $O$ at the center of line joining $AB$ and $CD$ (see figure). It is given a light push so that it starts rolling with its center $O$ moving parallel to $CD$ in the direction shown. As it moves, the roller will tend to :

go straight
turn left and right alternately
turn left
turn right

Solution

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