Question

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

Answer 1

Answer:

Situation is shown in figure. Let initially point of contact with ground is P , then after half revolution, point shift to top of the wheel at P' as you can see in figure.

so, displacement = final position - initial position

= PP' [ see figure ]

= √{length of half revolution² + diameter ²}

length of half revolution = πr = 3.14 × 1 = 3.14 m

diameter = 2r = 2 × 1 = 2m

so, displacement = √{3.14² + 2²}

= √{9.8596 + 4}

= √{13.8596} = 3.72 m

hence, The magnitude of the displacement of the point of the wheel initially in contact with ground is 3.72m