Answer:
The plank moves 0.2m from it's original position
Explanation:
we can do this question from the constraints that ,
- the wheel and the axle have the same angular speed or velocity
- the speed of the plank is equal to the speed of the axle at the topmost point .
thus ,
since the wheel is pure rolling or not slipping,
⇒[tex]v=wr[/tex]
where
[tex]v[/tex] - speed of the wheel
[tex]w[/tex] - angular speed of the wheel
[tex]r[/tex] - radius of the wheel
since the wheel traverses 1 m let's say in time '[tex]t[/tex]' ,
[tex]v_{w}=\frac{distance}{time} =\frac{1}{t}[/tex]
∴
⇒[tex]w=\frac{v_{w}}{r} = \frac{1}{t*0.25}[/tex]
the speed at the topmost point of the axle is :
⇒[tex]v_{a}=w*r\\v_{a}=\frac{1}{t*0.25} *0.05\\v_{a}=\frac{1}{5t}[/tex]
this is the speed of the plank too.
thus the distance covered by plank in time '[tex]t[/tex]' is ,
⇒[tex]d=v_{a}*t\\d=\frac{1}{5t} *t\\d=\frac{1}{5} = 0.2m[/tex]
