A uniform rope of length I lies on a table. If the coefficient of friction is ,then the maximum length 1₁ of the part of this rope which can overhang from the edge of the table without sliding down is...
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Answer:
Let mass of chain=M
Let the length of the hanging portion is x. Then the forces acting on the chain are
w = weight of the hanging part
=(
l
M
x)g
W = weight of the portion lying on the table
=(
l
M
g)(l−x)
w=(f
s
)
max
=μ
s
N
or (
l
M
g)x=μ
x
l
M
(l−x)g
⇒
l
x
=μ
x
[
l
l−x
] or
l
x
=μ
x
[1−
l
x
]
⇒
l
x
=mu
s
−μ
s
l
x
⇒(1+μ
s
)
l
x
=μ
s
x=
1+μ
s
μ
s
l
or x=
1+μ
μl
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