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(C) The linear displacement $S$ of a point on the rim of a rotating wheel is given by $S = r 	heta$,where $r$ is the radius and $	heta$ is the angul

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$y = 2x$

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(C) The linear displacement $S$ of a point on the rim of a rotating wheel is given by $S = r 	heta$,where $r$ is the radius and $	heta$ is the angular displacement.Since both wheels are fixed coaxially,they rotate together,meaning they have the same angular displacement $	heta$ in the same time interval.Let $r$ be the radius of the smaller wheel (supporting $A$) and $2r$ be the radius of the larger wheel (supporting $B$).The distance travelled by $A$ is $x = r 	heta$.The distance travelled by $B$ is $y = (2r) 	heta$.Dividing the two equations,we get $\frac{x}{y} = \frac{r 	heta}{2r 	heta} = \frac{1}{2}$.Therefore,$y = 2x$.

The figure shows a small wheel fixed coaxially on a bigger one of double the radius. The system rotates about the common axis. The strings supporting $A$ and $B$ do not slip on the wheels. If $x$ and $y$ are the distances travelled by $A$ and $B$ in the same time interval,then

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