The following four wires of length L and radius r are made of the same material .Which of these will have the largest extension,when the same tension is applied?

Options

A. L=100 cm,r=0.2 mm
B. L=200 cm, r=0.4 mm
C. L=300 cm,r=0.6 mm
D. L=400 cm,r=0.8 mm

Answer

A

Explanation

Young.s modulus, `Y=(F)/(A)(L)/(DeltaL)=(T)/(pir^(2))(L)/(DeltaL)`
or `DeltaL=(T)/(pir^(2))(L)/(Y)`
Where the symbols have their usual meaning As the wires are made of the same material,therefore Young.s modulus is the same four wires.As the T and Y are the same for the four wires.
`therefore DeltaLprop(L)/(r^(2))`
`(L)/(r^(2))` is maximum for wire of length L=100 cm and radius r=0.2 mm.