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Q.

A uniform rope of length L lies on a table. If the coefficient of friction is $μ$ , the maximum length of the hanging part of the rope from the edge of the table without sliding down is

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a

$\frac{(μ + 1) L}{μ}$

b

$\frac{μ L}{μ - 1}$

c

$\frac{μ L}{μ + 1}$

d

$μ L$

answer is D.

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Detailed Solution

In the critical case, weight of the hanging part = force of friction on the part of rope lying on table

$∴ \frac{m}{l} . l_{1} g = μ \frac{m}{l} (l - l_{1}) g$

Solving this, we get $l_{1} = (\frac{μ}{1 + μ}) l$

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A uniform rope of length L lies on a table. If the coefficient of friction is μ, the maximum length of the hanging part of the rope from the edge of the table without sliding down is