Question

A point $P$ consider at contact point of a wheel on ground which rolls on ground without slipping then value of displacement of point $P$ when wheel completes half of rotation (If radius of wheel is $1m$) :-

• A. $2m$
• B. $\sqrt{{\pi }^2+4}m$
• C. $\pi m$
• D. $\sqrt{{\pi }^2+2}m$

Answer 1

Answer: (B)

In half rotation point $P$ has moved horizontally.
$\frac{\pi d}{2}=\pi r=\pi \times 1m=\pi m.[\because$ radius $=1m]$
In the same time, it has moved vertically a distance which is equal to its diameter $=2m$.
$\therefore$ Displacement of $P=\sqrt{{\pi }^2+2^2}=\sqrt{{\pi }^2+4}m$.