Question

A uniform rope so lies on a table that part of it lays over.The rope begins to slide when the length of hanging part is 25 % of entire length. The co-efficient of friction between rope and table is

• A. 0.33
• B. 0.25
• C. 0.5
• D. 0.2

Answer 1

Answer: (A)

0.33

Answer is A.
Friction is the retarding force coming into play when two bodies are in contact with each other.
Friction formula in general is given by $F_f=\mu F_n$.
Where $F_f$ is the magnitude of friction, $\mu$ is the coefficient of friction and $F_n$ is the magnitude of normal force.
The Normal force = Weight of the given body. Hence Normal force Fn is given by
$F_n=mg$
Where m is the mass of the body and g is the gravity.
Friction formula is used to calculate the friction between the any two given bodies.
In this case, 1/4 th of the length L of the rope is hanging outside the table. So, the coefficient of friction is given by the equation as follows.
$\frac{L}{4}\times mg=\mu \times \frac{3L}{4}mg$.
Therefore, $\mu =\frac{1}{3}=0.33$
Hence, the co-efficient of friction between rope and table is 0.33