Rotational Motion Question 48
Question: P is the point of contact of a wheel and the ground. The radius of wheel is 1 m. The wheel rolls on the ground without slipping. The displacement of point P when wheel completes half rotation is:
[AIPMT 2002]
Options:
A) 2 m
B) $ \sqrt{{{\pi }^{2}}+4}m $
C) $ \pi m $
D) $ \sqrt{{{\pi }^{2}}+2}m $
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Answer:
Correct Answer: B
Solution:
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When the wheel rolls on the ground without slipping and completes half rotation, point P takes new. 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}+4R^{2}} $
But $ R=1m $ (given)
$ \therefore $ $ s=\sqrt{{{\pi }^{2}}{{(1)}^{2}}+4{{(1)}^{2}}} $ $ =\sqrt{{{\pi }^{2}}+4}m $
