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← JEE Main 2016 · 3 Apr · Shift 1
PhysicsSingle correct+4 / -1Question 5 of 90

JEE Main 2016 · 3 Apr · Shift 1, Physics question 5

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 :

Top view: a roller of two cones joined at their vertices O, its axis horizontal; rail CD is straight and perpendicular to the axis on the right, rail AB on the left is slanted so that it comes closer to O in the direction of motion (arrow up).
Choose one option
Answer and worked solution

Official answer: A

The cones narrow towards O. As the roller moves forward, rail AB comes closer to O, so on that side the roller rests on a smaller radius, while on rail CD the radius stays the same. Both cones turn at the same angular speed, so the AB (left) side covers less ground and the roller turns left.