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Mechanical Properties Of Fluids

Question

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Derive an expression for the increase in the length of a uniform rope hanging from the ceiling of a room, due to its own weight.

Solution

Let,
Mass of the wire = M
Area of cross section = A
Length of the rope = L
Let, l be the increase in the length of rope due to its own weight.
Since the rope is uniform and whole of the weight of rope can supposed to be concentrated at the centre of gravity, therefore the effective length of the rope is L/2 loaded by weight Mg.
Thus, Young's modulus is given by,

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