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Q.

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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a

$2 R$

b

$R \sqrt{1 + π^{2}}$

c

$R \sqrt{4 + π^{2}}$

d

$2 R \sqrt{1 + 4 π^{2}}$

answer is C.

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Detailed Solution

From figure,
Question Image
Displacement,
$B A = \sqrt{{(2 R)}^{2} + {(π R)}^{2}} = R \sqrt{4 + π^{2}}$

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