Two wires A and B are made of same material having ratio of lengths (L_A)/(L_B)=(1)/(3) and their diameters ratio (d_A)/(d_B)=2 . If both the wires are stretched using same force, what would be the ratio of their

Correct answer: B. 1: 12 L_ A L_ B =(1)/(3) and d_ A d_ B =2 Δ L_ A = F_ A L_ A A_ A Y_ A and Δ L_ B = F_ B L_ B A_ B Y_ B Given, F_A=F_B and Y_A=Y_B Δ L_ A Δ L_ B = F_ A L_ A A_ A Y_ A F_ B L_ B A_ B Y_ B =( L_ A L_ B )( A_ B A_ A ) Δ L_ A Δ L_ B =( L_ A L_ B )( (π)/(4) ~d_ B ^2 (π)/(4) ~d_ A ^2 )=( L_ A L_ B ) ( d_ B d_ A )^2 Δ L_ A Δ L_ B = ((1)/(3))((1)/(2))^2=(1)/(12)

JEE Main 20257 AprilMorning Shift

Exam: JEE Main
Year: 2025
Date: 7 April
Shift: Morning Shift
Subject: Physics
Chapter: Mechanical Properties of Solids

JEE Main 2025 · 7 April · Morning Shift · Physics · Mechanical Properties of Solids

Two wires A and B are made of same material having ratio of lengths...

Two wires A and B are made of same material having ratio of lengths

\frac{L_A}{L_B}=\frac{1}{3}

and their diameters ratio

\frac{d_A}{d_B}=2

. If both the wires are stretched using same force, what would be the ratio of their respective elongations?

Options

A $1: 6$
B $1: 12$
C $3: 4$
D $1: 3$

Correct answer

B. $1: 12$

Step-by-step solution

\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{1}{3}

and

\frac{\mathrm{d}_{\mathrm{A}}}{\mathrm{d}_{\mathrm{B}}}=2

\Delta \mathrm{L}_{\mathrm{A}}=\frac{\mathrm{F}_{\mathrm{A}} \mathrm{L}_{\mathrm{A}}}{\mathrm{A}_{\mathrm{A}} \mathrm{Y}_{\mathrm{A}}}

and

\Delta \mathrm{L}_{\mathrm{B}}=\frac{\mathrm{F}_{\mathrm{B}} \mathrm{L}_{\mathrm{B}}}{\mathrm{A}_{\mathrm{B}} \mathrm{Y}_{\mathrm{B}}}

Given,

F_A=F_B

and

Y_A=Y_B

\frac{\Delta \mathrm{L}_{\mathrm{A}}}{\Delta \mathrm{L}_{\mathrm{B}}}=\frac{\frac{\mathrm{F}_{\mathrm{A}} \mathrm{L}_{\mathrm{A}}}{\mathrm{A}_{\mathrm{A}} \mathrm{Y}_{\mathrm{A}}}}{\frac{\mathrm{F}_{\mathrm{B}} \mathrm{L}_{\mathrm{B}}}{\mathrm{A}_{\mathrm{B}} \mathrm{Y}_{\mathrm{B}}}}=\left(\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}\right)\left(\frac{\mathrm{A}_{\mathrm{B}}}{\mathrm{A}_{\mathrm{A}}}\right)

\frac{\Delta \mathrm{L}_{\mathrm{A}}}{\Delta \mathrm{L}_{\mathrm{B}}}=\left(\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}\right)\left(\frac{\frac{\pi}{4} \mathrm{~d}_{\mathrm{B}}^2}{\frac{\pi}{4} \mathrm{~d}_{\mathrm{A}}^2}\right)=\left(\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}\right)

\left(\frac{\mathrm{d}_{\mathrm{B}}}{\mathrm{d}_{\mathrm{A}}}\right)^2

<br/>

\frac{\Delta \mathrm{L}_{\mathrm{A}}}{\Delta \mathrm{L}_{\mathrm{B}}}=

\left(\frac{1}{3}\right)\left(\frac{1}{2}\right)^2=\frac{1}{12}

Practice Mechanical Properties of Solids on Quantrex Academy →

More from Mechanical Properties of Solids

Figure represents the extension ( Δ l ) of a wire of length 1 meter, suspended from the… JEE Main 2026 A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the… JEE Main 2026 The two wires A and B of equal cross-section but of different materials are joined… JEE Main 2026 A copper wire of length 3 m is stretched by 3 mm by applying an external force. The… JEE Main 2026 The Young's modulus of steel wire of radius r and length L is Y . If the radius r and… JEE Main 2026 Two wires as shown in the figure below, made of steel and have breaking stress of 12 ×… JEE Main 2026 A cube has side length 5 cm and modulus of rigidity 10^5 N/m ^2 . The displacement… JEE Main 2026 A metal string A is suspended from a rigid support and its free end is attached to a… JEE Main 2026 Full Mechanical Properties of Solids list All JEE Main PYQs