First slide

Friction on horizontal surface

Question

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

Moderate

A

$\frac{L}{μ}$
B

$\frac{L}{μ + 1}$
C

$\large \frac{\mu }{\mu + 1}$
D

$\large \frac{\mu L }{\mu + 1}$

Solution

Suppose Length of the hanging part is 'x' . Therefore length of chain lying on the table is (L-x). If λ be the mass per unit length of the chain , then
λx.g = µ(λ (L-x)g)
⇒ x/L = (µ / 1+µ )

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