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 $1 \,m$) :-

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