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  4. 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

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Q. 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

AMUAMU 2002

Solution:

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

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