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 m (given) \[\therefore s=\sqrt{{{\pi }^{2}}{{(1)}^{2}}+4{{(1)}^{2}}}\] \[=\sqrt{{{\pi }^{2}}+4}\,m\]You need to login to perform this action.
You will be redirected in
3 sec