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Question

# 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 :

A
θ=cos1(rR)
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B
θ=cos1(2rR)
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C
θ=cos1rR
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D
θ=sin1(rR)
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Solution

## The correct option is A θ=cos−1(rR)If the spool is not to translate,Fcosθ=f ....(i)If the spool is not to rotate,fR=Fr .....(ii)or fRrcosθ=for cosθ=rR⇒θ=cos−1(rR)Also the line of action of F should pass through the bottom most point.

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