Rotation Ques 2
- A roller is made by joining together two corners at their vertices $O$. It is kept on two rails $A B$ and $C D$ which are placed asymmetrically (see the figure), with its axis perpendicular to $C D$ and its centre $O$ at the centre of line joining $A B$ and $C D$ (see the figure). It is given a light push, so that it starts rolling with its centre $O$ moving parallel to $C D$ in the direction shown. As it moves, the roller will tend to
(2016 Main)
(a) turn left
(b) turn right
(c) go straight
(d) turn left and right alternately
Show Answer
Answer:
Correct Answer: 2.( a )
Solution:
At distance $x_0$ from $O, v=\omega R$
Distance less than $x_0, v>\omega R$
Initially, there is pure rolling at both the contacts. As the cone moves forward, slipping at $A B$ will start in forward direction, as radius at left contact decreases.
Thus, the cone will start turning towards left. As it moves, further slipping at $C D$ will start in backward direction which will also turn the cone towards left.
BETA
