A) \[2\pi \]
B) \[\sqrt{2\pi }\]
C) \[\sqrt{{{\pi }^{2}}+4}\]
D) \[\pi \]
Correct Answer: C
Solution :
When wheel rolls half a revolution, the point (P) of the wheel which is in contact with the ground initially, moves at the top of the wheel as shown. Horizontal displacement of wheel, \[x=\pi r,\]where r being the radius. Vertical displacement of point P, \[y=2r\] Net displacement\[=\sqrt{{{x}^{2}}+{{y}^{2}}}\] \[=\sqrt{{{(\pi r)}^{2}}+{{(2r)}^{2}}}\] \[=r\sqrt{{{\pi }^{2}}+4}\] \[=\sqrt{{{\pi }^{2}}+4}\] \[(\because \,r=1\,m)\]You need to login to perform this action.
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