Question

The spool shown in figure is placed on a rough horizontal surface has inner radius r and outer radius R.

The angle θ between tha 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 = cos^-1(r/R)

(B)  θ = cos^-1(2r/R)

(C)  θ = cos^-1√(r/R)

(D)  θ = sin^-1√(r/R)

Answer 1

Correct option (A)  θ = cos^-1(r/R)

Explanation:

If spool is not to translate,

Fcos θ = f ...(1) 

If spool is not to rotate,

Fr = fR

From eq. (1) and (2) we get static friction