Question

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

• A. $0.33$
• B. $0.25$
• C. $0.5$
• D. $0.2$

Answer 1

The correct option is A $0.33$

Let the total length of the rope be 'x' and, mass per unit length of the rope be 'm'

So, the length of the hanging rope = $=\frac{25}{100}x=0.25x$

Mass of the hanging part of the rope = $0.25xm$

Mass of the rope on the table = $\frac{75}{100}xm=0.75xm$

Let the coefficient of friction between the rope and the table be $\mu$

Using equation of motion,

weight of rope on the table = weight of the hanging rope

$\mu \left(0.75\right)mxg=0.25mgx\Rightarrow \mu =0.33$