The following four wires 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)`
`DeltaL = (T)/(pir^(2)) (L)/(Y)`
Where the symbols have their usual meainings.
As the four wires are made of the same material, therefore Young's modulus is the same for four wires.
As the T and Y are the same for the four wires.
`therefore " " DeltaL prop (L)/(r^(2))`
`(L)/(r^(2))` is maximum for wire of lenght L = 100 cm and radius r = 0.2 mm.