A uniform chain of length $L$ is lying partly on a table, the remaining part hanging down from the edge of the table. If the coefficient of friction between the chain and the table is $0.5$, what is the minimum length of the chain that should lie on the table, to prevent the chain from slipping down to the ground?
- $L/3$
- $L/2$
- $2L/3$
- $3L/4$
The Correct Option is C
Solution and Explanation
Mass per unit length of the chain = $\frac{M}{L}$
Mass of length x of the chain = $\frac{M}{L}x$
Mass of the length $(L - x)$ of hanging chain = $\frac{M}{L} (L -x)$
At equilibrium, friction force between table and chain
= weight of hanging part of chain
$\mu\left(\frac{M}{L}x\right)g =\frac{M}{L}\left(L -x\right)g$
$0.5\: x =L - x ; 1.5 \, x = L$
$\therefore \:\:\: x = \frac{2L}{3}$
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Concepts Used:
Laws of Motion
The laws of motion, which are the keystone of classical mechanics, are three statements that defined the relationships between the forces acting on a body and its motion. They were first disclosed by English physicist and mathematician Isaac Newton.
Newton’s First Law of Motion
Newton’s 1st law states that a body at rest or uniform motion will continue to be at rest or uniform motion until and unless a net external force acts on it.
Newton’s Second Law of Motion
Newton's 2nd law of motion deals with the relation between force and acceleration. According to the second law of motion, the acceleration of an object as built by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.
Newton’s Third Law of Motion
Newton's 3rd law of motion states when a body applies a force on another body that there is an equal and opposite reaction for every action.