A, B and C are three identical solid cylinders of radius R are placed on a rough horizontal ground with their axes are parallel to each other. A wooden scale is placed above ABC as shown in fig. There is no slip at any contact and there is no collision between cylinders. The scale is moved such the cylinders rotate one rotation then the displacement of the tip "P” of the scale with respect to the ground is

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$4 π R$

$2 π R$

$6 π R$

$3 π R$

answer is B.

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Detailed Solution

Since there is no slip at any content. As the lower and upper contants of any cylinder, we get a displacement of $2 π R$ for the center of mass of the cylinder with respect to the ground, and another $2 π R$ for the scale with respect to the cylinder. Net displacement the scale with respect to the ground is $2 π R + 2 π R = 4 π R$ it is independent of no. of cylinders.