Question

A massless spool of inner radius $r$, outer radius $R$ is placed against vertical wall and tilted split floor as shown. A light inextensible thread is tightly wound around the spool through which a mass $m$ is hanging. There exists no friction at point $A$, while the coefficient of friction between spool and point $B$ is $\mu$. The angle between two surfaces is $\rho$

• A. the magnitude of force on the spool at $B$ in order to maintain equilibrium is $mg\sqrt{{\left(\frac{r}{R}\right)}^2+{(1-\frac{r}{R})}^2\frac{1}{{\tan }^2\theta }}$
• B. the magnitude of force on the spool at $B$ in order to maintain equilibrium is $mg(1-\frac{r}{R})\frac{1}{{\tan }^{}\theta }$
• C. the minimum value of $mu$ for the system to remain in equilibrium is $\frac{\cot \theta }{\left(R/r\right)-1}$
• D. the minimum value of $\mu$ for the system to remain in equilibrium is $\frac{\tan \theta }{\left(R/r\right)-1}$

Answer 1

Answer: (A), (B)

The correct options are
A the magnitude of force on the spool at $B$ in order to maintain equilibrium is $mg\sqrt{{\left(\frac{r}{R}\right)}^2+{(1-\frac{r}{R})}^2\frac{1}{{\tan }^2\theta }}$
B the magnitude of force on the spool at $B$ in order to maintain equilibrium is $mg(1-\frac{r}{R})\frac{1}{{\tan }^{}\theta }$