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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: go straight, Turn right, Turn left, Turn left and right alternately

go straight

Turn right

Turn left

Turn left and right alternately

Solution:

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=rω, the roller will turn to left.