Question:
Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area A and wire 2 has cross-sectional area 3A. If the length of wire 1 increases by Δ x on applying force F, how much force is needed to stretch wire 2 by the same amount?
Two wires are made of the same material and have the same volume. However wire 1 has cross-sectional area A and wire 2 has cross-sectional area 3A. If the length of wire 1 increases by Δ x on applying force F, how much force is needed to stretch wire 2 by the same amount?
Show Hint
For same material, extension depends on (FL)/(A).
Updated On: Mar 20, 2026
- \(4F\)
- \(6F\)
- \(9F\)
- F
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Extension of a wire: Δ x = (FL)/(AY)
Step 2: Same volume implies: A₁L₁ = A₂L₂ ⟹ L₂ = (L₁)/(3)
Step 3: For same extension: (F₁L₁)/(A₁Y) = (F₂L₂)/(A₂Y) ⟹ F₂ = 9F₁
Was this answer helpful?
0
0
Top Questions on Stress and Strain
- A brass wire of length $2\,\text{m}$ and radius $1\,\text{mm}$ at $27^\circ\text{C}$ is held taut between two rigid supports. Initially it was cooled to a temperature of $-43^\circ\text{C}$ creating a tension $T$ in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to $1.4T$ is ___$^\circ$C.
- JEE Main - 2026
- Physics
- Stress and Strain
- One end of a steel wire is fixed to the ceiling of an elevator moving up with an acceleration \( 2 \, \text{m/s}^2 \) and a load of 10 kg hangs from the other end. If the cross-section of the wire is \( 2 \, \text{cm}^2 \), then the longitudinal strain in the wire will be (Take \( g = 10 \, \text{m/s}^2 \) and \( Y = 2.0 \times 10^{11} \, \text{N/m}^2 \)).
- WBJEE - 2025
- Physics
- Stress and Strain
- The total energy of a satellite in a circular orbit at a distance \( (R + h) \) from the center of the Earth varies as
- KCET - 2025
- Physics
- Stress and Strain
- For smaller deformations, stress is directly proportional to the strain for any material. Then the constant of proportionality is called as its
- KEAM - 2025
- Physics
- Stress and Strain
- Young's modulus and shear modulus are applicable for:
- KEAM - 2025
- Physics
- Stress and Strain
View More Questions
Questions Asked in BITSAT exam
- Evaluate the integral \( \int \frac{x}{x^2 + 1} dx \):
- BITSAT - 2025
- Methods of Integration
- Evaluate the integral \( \int_0^1 \frac{\ln(1 + x)}{1 + x^2} \, dx \)
- BITSAT - 2025
- integral
- The equation of the line passing through the point $ (2, 3) $ and making equal intercepts on the coordinate axes is:
- BITSAT - 2025
- Coordinate Geometry
- If $ x + \frac{1}{x} = 4 $, find the value of $ x^4 + \frac{1}{x^4} $.
- BITSAT - 2025
- Differential equations
- If the word "BITS" is coded using \( A=1, B=2, \ldots, Z=26 \), and the code is the sum of the squares of each letter's value, what is the code for the word?
- BITSAT - 2025
- Algebra
View More Questions