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 hanging part of the rope which can overhang from the edge of the table without sliding down is

Moderate

A

l/ $μ$
B

$l / (μ + 1)$
C

$μ l / (μ + 1)$
D

$μ l / (μ - 1)$

Solution

In critical case, weight of hanging part = force of friction of the part of rope lying on table.
$∴ \frac{m}{l} \cdot l_{1} g = μ \frac{m}{l} (l - l_{1}) g$
Solving above equation, we get
$l_{1} = (\frac{μ}{1 + μ}) l$

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