Question

A uniform rope lies on a table with some portion hanging. The rope begins to slide when the length of the hanging part is 25% of the entire length. The coefficient of friction between the rope and table is:

(A)0.33
(B)0.25
(C)0.50
(D)0.20

Answer 1

The coefficient of friction is calculated by equating the static friction force with the gravitational force of the hanging part of the rope. When the hanging part is 25% of the rope's total length, the frictional force matches this, which allows us to find that the coefficient of friction is 0.20.

Step-by-step explanation:

The question asks for the coefficient of friction between a rope and a table, which can be determined by using the concept of static friction and the forces acting on the rope when it begins to slide. As the rope slides off when the hanging part is 25% of its length, we can understand that the weight of the hanging part provides the force due to gravity that overcomes the static friction force between the rope and the table on the remaining 75%.

The static friction force (f_s) equals the coefficient of static friction (μ_s) multiplied by the normal force (N), which in this case is the weight of the portion of the rope on the table (75% of the total weight). The force due to gravity on the hanging part (25% of the total weight) equals the static friction force at the point of sliding. Therefore, we can set up the equation f_s = μ_s × N = Weight of the hanging part. Solving for μ_s, we find that the coefficient of static friction is 0.20.