Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2011
Exam
BITSAT
Year
2011
Subject
Physics
Chapter
Mechanical Properties of Solids

BITSAT 2011 · Physics · Mechanical Properties of Solids

Two wires are made of the same material and have the same volume....

Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area AA and wire 2 has cross-sectional area 3A3 A. If the length of wire 1 increases by Δx\Delta x on applying force F,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 crosssectional area A and wire 2

Options

  1. A4F4 F
  2. B6F6 F
  3. C9F9 F
  4. DFF

Correct answer

C. 9F9 F

Step-by-step solution

Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area A and wire 2
As shown in the figure, the wires will have the same Young's modulus (same material) and the length of the wire of area of crosssection 3A3 A will be ℓ/3\ell / 3 (samevolume as wire 1 ). For wire 1,Y=F/AΔx/ℓ1, \quad Y=\frac{F / A}{\Delta x / \ell} For wire 2,Y=F′/3AΔx/(ℓ/3)2, Y=\frac{F^{\prime} / 3 A}{\Delta x /(\ell / 3)} From (i) and (ii) ,FA×ℓΔx=F′3A×ℓ3Δx⇒F′=9F, \frac{F}{A} \times \frac{\ell}{\Delta x}=\frac{F^{\prime}}{3 A} \times \frac{\ell}{3 \Delta x}\Rightarrow F^{\prime}=9 F
Practice Mechanical Properties of Solids on Quantrex Academy →

More from Mechanical Properties of Solids

Two wires of the same material (Young's modulus =Y ) and same length L but radii R and 2… BITSAT 2024With rise in temperature, the Young's modulus of elasticity: BITSAT 2024Young's modules of materials of a wire of Length ' L ' and cross-sectional area A is Y.… BITSAT 2024Young's moduli of the material of wires A and B are in the ratio of 1: 4 , while its area… BITSAT 2023A 100 m long wire having cross-sectional area 6.25 × 10^ -4 m^2 and Young's modulus is… BITSAT 2023There are two wire of same material and same length while the diameter of second wire is… BITSAT 2020A steel wire of cross-sectional area 4 cm ^ 2 has elastic limit of 2. 2 × 10 ^ 8 Nm^ - 2… BITSAT 2019A rubber cord has a cross-sectional area 10 ^ - 6 m^ 2 and total unstretched length 0. 1m… BITSAT 2019 Full Mechanical Properties of Solids list All BITSAT PYQs