The spool shown in figure is placed on a rough horizontal surface 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

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 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= cos -1((r/R)) (B) θ= cos -1((2 r/R)) (C) θ= cos -1 √(r/R) (D) θ= sin -1((r/R))

Tardigrade Admin · Accepted Answer

Correct answer is (a) θ= cos -1((r/R))

Q. The spool shown in figure is placed on a rough horizontal surface 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

$θ = cos^{- 1} (\frac{r}{R})$

$θ = cos^{- 1} (\frac{2 r}{R})$

$θ = cos^{- 1} \frac{r}{R}$

$θ = sin^{- 1} (\frac{r}{R})$

Correct answer is (a) $θ = cos^{- 1} (\frac{r}{R})$

Q. The spool shown in figure is placed on a rough horizontal surface 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

θ=cos−1(Rr​)

θ=cos−1(R2r​)

θ=cos−1Rr​​

θ=sin−1(Rr​)