A) 2 m
B) \[\sqrt{{{\pi }^{2}}+4}\,m\]
C) \[\pi \,m\]
D) \[\sqrt{{{\pi }^{2}}+2}\,m\]
Correct Answer: B
Solution :
When the wheel rolls on the ground without slipping and completes half rotation, point P takes new position as P as shown in figure. Horizontal displacement, \[x=\pi R\] |
Vertical displacement, \[y~=2R\] |
Thus, displacement of the point P when wheel completes half rotation, |
\[s=\sqrt{{{x}^{2}}+{{y}^{2}}}\] |
\[=\sqrt{{{(\pi R)}^{2}}+{{(2R)}^{2}}}\] |
\[=\sqrt{{{\pi }^{2}}{{R}^{2}}+4{{R}^{2}}}\] |
But \[R=1\text{ }m\] (given) |
\[\therefore \] \[s=\sqrt{{{\pi }^{2}}{{(1)}^{2}}+4{{(1)}^{2}}}\] |
\[=\sqrt{{{\pi }^{2}}+4}\,m\] |
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