Two thin circular disks of mass $2 k g$ and radius $10 c m$ each are joined by a rigid massless rod of length $20 c m$ . The axis of the rod is perpendicular to the planes of the disk through their centres as shown in the Figure. This object is kept on a truck in such a way that the axis of the object is horizontal and perpendicular to the direction of the motion of the truck. Its friction with the floor of the truck is large enough so that the object can roll on the truck without slipping. Take the $x - a x i s$ as the direction of motion of the truck and the $z - a x i s$ as the vertically upward direction. If the truck has an acceleration of $9 m / s^{2}$ , calculate the force of friction on each disk.

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$(9 \hat{i}) N$

$(6 \hat{i}) N$

$(2 \hat{i}) N$

$(3 \hat{i}) N$

answer is B.

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Detailed Solution

In the reference frame of the truck, frictional force will pull the disks in the direction of motion of the truck, while pseudo force $(F = m a)$ , where $a = 9 m / s^{2}$ acts in the backward direction of motion of the truck. Consider the forces on either wheel. For the translation of the disk.