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 :

Option 1)

 turn left.

Option 2)

 turn right.

Option 3)

go straight

Option 4)

 turn left and right alternately.

Answers (1)
V Vakul

As we learnt in

Rolling motion -

V_{cm}= Rw\rightarrow pure \: rolling

V_{cm}> Rw\rightarrow slipping \: motion

V_{cm}< Rw\rightarrow skidding \: motion

-

 

 

The distance of central line from instantaneous axis of rotation is r

r_{left}=\omega 'r<\omega r=v_{right}

So the roller will turn to left.


Option 1)

 turn left.

This is the correct option.

Option 2)

 turn right.

This is an incorrect option.

Option 3)

go straight

This is an incorrect option.

Option 4)

 turn left and right alternately.

This is an incorrect option.

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