JEE Main · 2019 · 08 Apr 2019 · Shift 2 · Elasticity & SHM

Young's moduli of two wires

A

and

B

are in the ratio

7 : 4

. Wire

A

is 2 m long and has radius

R

. Wire

B

is 1.5 m long and has radius 2 mm. If the two wires stretch by the same length for a given load, then the value of

R

is close to:

Answer: (C)

Solution

For a stretched wire

Y = \frac{F / A}{ℓ / L}

, so the elongation is

ℓ = \frac{F L}{A Y}

. Both wires feel the same load

F

and are to stretch by the same amount

ℓ

, so

\frac{L _{A}}{A _{A} Y _{A}} = \frac{L _{B}}{A _{B} Y _{B}}

. Writing each area as

π R^{2}

(the

π

cancels) and using

Y_{A} : Y_{B} = 7 : 4

with

L_{A} = 2 m

L_{B} = 1.5 m

and

R_{B} = 2 mm

, we get

R^{2} = \frac{L _{A} Y _{B} R _{B}^{2}}{L _{B} Y _{A}} = \frac{2 \times 4 \times 4}{1.5 \times 7} = \frac{32}{10.5} \approx 3.05 mm^{2}

. Taking the square root,

R \approx 1.7 mm

JEE Main · 2019 · 08 Apr 2019 · Shift 2 · Single correct option