A uniform rope of length l 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

Question

A uniform rope of length l 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 (A) (1/μ ) (B) (l/μ + 1) (C) (μ l/1 + μ ) (D) (μ l/1 - μ )

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-9i5vqf6b3jpk.png" /> Weight of hanging part is balanced by friction (m (l1/l))g=μ N (m (l1/l))g=μ (m (l - l1/l))g l1=μ (l - l1) l1=(μ l/μ + 1)

Q. A uniform rope of length $l$ lies on a table. If the coefficient of friction is $μ$ , then the maximum length $l_{1}$ of the part of this rope which can overhang from the edge of the table without sliding down is

$\frac{1}{μ}$

$\frac{l}{μ + 1}$

$\frac{μ l}{1 + μ}$

$\frac{μ l}{1 - μ}$

Weight of hanging part is balanced by friction
$(m \frac{l _{1}}{l}) g = μ N$
$(m \frac{l _{1}}{l}) g = μ (m \frac{l - l _{1}}{l}) g$
$l_{1} = μ (l - l_{1})$
$l_{1} = \frac{μ l}{μ + 1}$

Q. A uniform rope of length l 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

μ1​

μ+1l​

1+μμl​

1−μμl​