question_answer

A wheel of radius 1 m rolls forward half a revolution on a horizontal ground. The magnitude of the displacement of the point of wheel initially in contact with the ground is

A) \[2\pi m\]                           

B)  \[\sqrt{2}\pi m\]

C) \[\sqrt{{{\pi }^{2}}+4}m\]            

D)  \[\pi \,m\]

Correct Answer: C

Solution :

                 After half a revolution, vertical distance travelled by point\[=\frac{1}{2}\] times circumference of wheel\[=\pi r\]\[=\pi \] metre                                Total displacement of point\[=\sqrt{{{\pi }^{2}}+{{2}^{2}}}=\sqrt{{{\pi }^{2}}+4}\]