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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.
PhysicsLaws of MotionJEE MainJEE Main 2022 (25 Jun Shift 1)
Solution:
1633 Upvotes Verified Answer
The correct answer is: 2

Let, λ=mass per unit length of the chain and length of mass hanging through the table is x.

Normal force applied by the table on the chain will be, N=l-xλg.

Tension developed in the chain will balance the gravitational force acting in the downward direction, T=λxg.

Maximum limiting force possible for the part of the table, fmax=μN=μl-xλg

For equilibrium,

fmax=T,

μl-xλg=λxg12×6-x=x x=2 m

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