A disc is rolling without slipping on a surface. The radius of the disc is $R .$ At $t = 0,$ the top most point on the disc is $A$ as shown in figure. When the disc completes half of its rotation, the displacement of point $A$ from its initial position is

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The displacement is the hypotenuse of the diameter and the distance travelled for half the rotation π R . By using Pythagoras theorem, Displacement of A = ( 2 R ) 2 + ( π R ) 2 = R π 2 + 4

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