Question

A rope lies on a table such that a part of it is hanging. The rope begins to slide when the length of the hanging part is 25% of the entire length. What is the coefficient of friction between the rope and the table?

• A. 0.2
• B. 0.33
• C. 0.5
• D. 0.75

Answer 1

The correct option is B 0.33

Suppose l is the length of the hanging part and the total length of the rope is L, then coefficient of friction is given by:
Mass per unit length is $\frac{m}{L}$.
Mass of the part on the table $=\frac{m}{L}(L-l)$.
Mass of the hanging part $=\frac{m}{L}\left(l\right)$.
Friction balances the weight of the part that is hanging.
$\mu \frac{m}{L}(L-l)g=\frac{m}{L}\left(l\right)g$
$\mu =\frac{l}{L-l}$
$\mu =\frac{l}{L-l}=\frac{0.25L}{L-0.25L}=\frac{1}{3}$