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Question

# A uniform wire of length 1 m and radius 0.028 cm is employed to raise a stone of density 2500 kg/m3 immersed in water. Find the change in elongation of wire when the stone is raised out of water. [massofstone=5 kg, Yofmaterialofwire=2×1011 N/m2]

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Solution

## When a stone is raised from water wright increases as the buoyant force extingushes i.e., the change in force equal to the buoyant force being applied by water an the stone.As buoyant forceFL=lfVg where, lf=density of displaced field Fb=1000×(52500)× V= volume of field displaced [lf=1000kg/m3]Fb=2gthen, bu Youngls modulusY=F/AΔl/l2×1011=2g/π(0.00028)2Δl/12×1011=2gπ×282×10−10ΔlΔl=2gπ×1011×π×28210−10Δl=2×102×π×282×10Δl=1π×282Δl=4.06×10−4mΔl=0.0406cmThus, the wire elongates by 0.0406cm in raising the rock from water.

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