Question 1:
difficultA 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 $1\text{ m}$):
(2002)
Horizontal displacement is $\pi R$ and vertical displacement is $2R$. Total displacement is given by $\sqrt{(pi R)^2 + (2R)^2} = R\sqrt{\pi^2+4}$, which evaluates to $\sqrt{pi^2+4}\text{ m}$ for $R = 1\text{ m}$.