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A chain of length ‘L’ is kept on a rough table(mew)with length ‘x’hanging beyond edge.What is maximum value of ‘x’ for equation?

A chain of length ‘L’ is kept on a rough table(mew)with length ‘x’hanging beyond edge.What is maximum value of ‘x’ for equation?

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1 Answers

Sumit Majumdar IIT Delhi
askIITians Faculty 137 Points
8 years ago
Dear student,
The mass per unit length of the string would be given by:
\frac{M}{L}
Hence, the mass of the chain that is kept on the table would be given by:
\frac{M\left ( L-x \right )}{L}
Thus, the frictional force acting on the chain kept on the surface would be given by:
\mu\frac{M\left ( L-x \right )}{L}g
The weight of the chain that is hanging would be given by:
\frac{Mx}{L}g
Hence, if the masses have to be balanced, then
\frac{Mx}{L}g=\mu\frac{M(L-x)}{L}g\Rightarrow x=\mu(L-x)\Rightarrow x=\frac{\mu L}{1+\mu}
Regards
Sumit

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