JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Elasticity & SHM

Young's moduli of the material of wires A and B are in the ratio of

1 : 4

, while its area of cross sections are in the ratio of

1 : 3

. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires

A

and

B

will be in the ratio of
[Assume length of wires A and B are same]

Answer: (B)

Solution

The elongation is given by

Δ L = \frac{F L}{A Y}

. For the same force

F

and length

L

\frac{Δ L _{A}}{Δ L _{B}} = \frac{A _{B}}{A _{A}} \times \frac{Y _{B}}{Y _{A}} = 3 \times 4 = 12

. Therefore, the ratio is

12 : 1

JEE Main · 2023 · 10 Apr 2023 · Shift 2 · Single correct option