Q.

The spool shown in the figure is placed on a rough horizontal surface and has inner radius r and outer radius R. The angle θ between the applied force and the horizontal can be varied. The critical angle (θ) for which the spool does not roll and remains stationary is given by

Moderate

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θ=cos−1⁡rR

θ=cos−1⁡2rR

θ=cos−1⁡rR

θ=sin−1⁡rR

answer is 1.

(Detailed Solution Below)

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Detailed Solution

If the spool is not to translate, Fcos⁡θ=f ……….(i)If the spool is not to rotate,Fr=fR …….(ii)or fRrcos⁡θ=for cos⁡θ=rR⇒θ=cos−1⁡rRAlso the line of action of F should pass through the bottom-most point.

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