A roller is made by joining together two cone | vedclass

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Question

(C) As shown in the diagram,the roller is placed on two rails $AB$ and $CD$. The rails are asymmetrical such that the distance from the axis of rotati

Vedclass · Accepted Answer

turn left

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(C) As shown in the diagram,the roller is placed on two rails $AB$ and $CD$. The rails are asymmetrical such that the distance from the axis of rotation to the point of contact on the left rail $AB$ is different from that on the right rail $CD$.Since the roller is composed of two cones joined at their vertices $O$,the radius of the roller at the point of contact with the rails depends on the distance from the vertex $O$.For a rolling motion,the linear velocity $v$ at any point of contact is given by $v = r \omega$,where $r$ is the radius of the cone at that point and $\omega$ is the angular velocity.Because the rails are placed asymmetrically,the effective radius $r$ at the contact point on the left rail is smaller than the effective radius $r$ at the contact point on the right rail.Since $v = r \omega$,the side with the smaller radius will have a smaller linear velocity,causing the roller to turn towards the side with the smaller radius,which is the left side.

Quantities	Their numerical values (in $SI$ units)
a. Angular acceleration of smaller wheel	$1$. $5/3$
b. Torque on the larger wheel	$2$. $100/3$
c. Angular acceleration of larger wheel	$3$. $5/2$

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