A wheel of radius 1 m rolls through 180^ over a plane surface. The magnitude of the displacement of the point of the wheel initially in contact with the surface is.

Step-by-step solution

Distance travelled by the wheel in half revolution = C 2 = 2 r 2 = r Where C is the circumference of the wheel. From figure, Displacement of initial point of contact after half revolution = AB array ll & A B^2=A D^2+ DB ^2 & A B^2=( r)^2+(2 r)^2=r^2 ( ^2+4 ) & A B=r ( ^2+4 ) & A B= ( ^2+4 ) array ...(given r=1 ~m )