Answer:
Approximately [tex]0.796[/tex] minutes.
Explanation:
Apply unit conversion and ensure that all distances are measured in standard units:
[tex]r = 40\; {\rm cm} = 0.40\; {\rm m}[/tex].
The circumference of this wheel is:
[tex]2\, \pi\, r = 2\, \pi\, (0.40\; {\rm m}) = 0.80\, \pi\; {\rm m}[/tex].
Thus, each revolution of the wheel would wind up [tex]0.80\, \pi\; {\rm m}[/tex] of cord.
Multiply the distance winded up per revolution by the rate of revolution to find the rate at which the cord is winded up:
[tex]\begin{aligned} & \frac{0.80\,\pi\; \text{meter}}{1\; \text{revolution}} \cdot \frac{5\; \text{revolution}}{1\; \text{minute}} = \frac{4\, \pi\; \text{meter}}{1\; \text{minute}}\end{aligned}[/tex].
Divide the length of the cord by this rate to find the time it takes to wind up the cord:
[tex]\begin{aligned}& \frac{10\; \text{meter}}{4\, \pi\; \text{meter}\cdot \text{minute}^{-1}} \\ =\; & \frac{2.5}{\pi}\; \text{minute} \\ \approx\; & 0.796\; \text{minute}\end{aligned}[/tex].
