First slide

Friction on horizontal surface

Question

A uniform rope of length I lies on a table. If the coefficient of friction is ' $μ$ ', then the maximum length l₁ of the part of this rope which can overhang from the edge of the table without sliding down is:

Easy

A

$\frac{1}{μ}$
B

$\frac{1}{μ + 1}$
C

$\frac{μl}{μ + 1}$
D

$\frac{μl}{μ - 1}$

Solution

weight of the hanging part = frictional force on the table
$i f l_{1} p a r t i s h a n g i n g i t s w e i g h t = \frac{M}{L} l_{1} g L - l_{1} i s o n t h e t a b l e a n d f r i c t i o n a l f o r c e d u e t o t h i s = μ \frac{M}{L} (L - l_{1}) g \frac{M}{L} l_{1} g = μ \frac{M}{L} (L - l_{1}) g l_{1} = μ (L - l_{1}) l_{1} (1 + μ) = μ L l_{1} = \frac{μ L}{1 + μ}$

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