A uniform chain of 6, m length is placed on a table such that a part of its length is hanging over e

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4-2.Friction

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A uniform chain of $6\, m$ length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is $0.5$, the maximum length of the chain hanging from the table is.......$m.$

$25$

$12$

$9$

$2$

(JEE MAIN-2022)

Mass per unit length $=\lambda$

$N = mg =\lambda( L – x ) g$

$fs _{\max }=\mu_{ s } N$

$fs _{\max }=(0.5)(\lambda)( L – x ) g$

And also $fs _{\max }= m _{ x } g$

$0.5 \lambda( L – x ) g =\lambda xg$

$\frac{ L – x }{2}= x$

$\frac{ L }{2}=\frac{3 x }{2} \Rightarrow x =\frac{ L }{3}=\frac{6}{3}=2 \,m$

Standard 11

Physics

medium

easy

easy

medium

medium