Two wires $A$ and $B$ made of different materials of length 6.0 cm and 5.4 cm, respectively and area of cross sections $3.0 \times 10^{-5} \mathrm{~m}^{2}$ and $4.5 \times 10^{-5} \mathrm{~m}^{2}$, respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of $A$ to that of $B$ is $\mathrm{x}: 3$. The value of x is \_\_\_\_.

JEE Main · 2026 · 28 Jan 2026 · Shift 1 · Elasticity & SHM

Two wires

A

and

B

made of different materials of length 6.0 cm and 5.4 cm, respectively and area of cross sections

3.0 \times 1 0^{- 5} m^{2}

and

4.5 \times 1 0^{- 5} m^{2}

, respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of

A

to that of

B

x : 3

. The value of x is ____.

Answer: (D)

Young's modulus:

Y = \frac{F ℓ}{A Δ ℓ}

Since the extension

Δ ℓ

and force

F

are the same for both wires:

\frac{Y _{A}}{Y _{B}} = \frac{ℓ _{A}}{ℓ _{B}} \cdot \frac{A _{B}}{A _{A}}

Substituting values:

\frac{Y _{A}}{Y _{B}} = \frac{6}{5.4} \times \frac{4.5 \times 1 0 ^{- 5}}{3 \times 1 0 ^{- 5}} = \frac{6}{5.4} \times 1.5 = \frac{5}{3}

Therefore:

x = 5

JEE Main · 2026 · 28 Jan 2026 · Shift 1 · Single correct option