MCQ Solution: Laws of Motion
A uniform rope of length l lies on a table. If the coefficient of friction is µ, then the maximum length l1 of the hanging part of the rope which can overhang from the edge of the table without sliding down is
1) l/µ
2) l/(µ+1)
3) µl/(µ+1)
4) µl/ (l-1)
Solution
To prevent sliding of rope
friction due to rope on table = weight of rope hanging
let m be the mass per unit length of rope. l1 be the length hanging
m(l-l1)gµ = l1mg
lµ - l1µ = l1
l1 ( 1+ µ) = lµ
l1 = lµ / ( 1+ µ)
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