A 100 m long wire having cross-sectional area 6.25 $\times 10^{-4} \mathrm{~m}^{2}$ and Young's modulus is $10^{10} \mathrm{Nm}^{-2}$ is subjected to a load of 250 N , then the elongation in the wire will be :

(D) $4 \times 10^{-3} \mathrm{~m}$

(A) $6.25 \times 10^{-3} \mathrm{~m}$

(B) $4 \times 10^{-4} \mathrm{~m}$

(C) $6.25 \times 10^{-6} \mathrm{~m}$

JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Elasticity & SHM

A 100 m long wire having cross-sectional area 6.25

\times 1 0^{- 4} m^{2}

and Young's modulus is

1 0^{10} Nm^{- 2}

is subjected to a load of 250 N , then the elongation in the wire will be :

Answer: (D)

The elongation of a loaded wire is

δ = \frac{F ℓ}{A Y}

. Substituting

F = 250 N

ℓ = 100 m

A = 6.25 \times 1 0^{- 4} m^{2}

and

Y = 1 0^{10} N/m^{2}

gives

δ = \frac{250 \times 100}{6.25 \times 1 0 ^{- 4} \times 1 0 ^{10}} = 4 \times 1 0^{- 3} m

JEE Main · 2023 · 24 Jan 2023 · Shift 1 · Single correct option