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Properties of Matter question

2023 · 10 Apr · Shift 2 · Q52
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Properties of Matter question

2023 · 10 Apr · Shift 2 · Q52

JEE MainPhysicsProperties of MatterMCQ+4 / −1
Young's moduli of the material of wires A and B are in the ratio of 1:41: 41:4, while its area of cross sections are in the ratio of 1:31: 31:3. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires A\mathrm{A}A and B\mathrm{B}B will be in the ratio of [Assume length of wires A and B are same]
  1. A
    1 : 12
  2. B
    1 : 36
  3. C
    12 : 1
  4. D
    36 : 1
View written solutionFree

Correct answer: C

  1. For a wire under load, the elongation is
ΔL=FLAY\Delta L = \frac{F L}{A Y}ΔL=AYFL​

where:

  • FFF = applied force,
  • LLL = length of wire,
  • AAA = cross-sectional area,
  • YYY = Young's modulus.
  1. Here, both wires have:
  • same load FFF,
  • same length LLL.

So,

ΔL∝1AY\Delta L \propto \frac{1}{A Y}ΔL∝AY1​
  1. Given ratios:
YA:YB=1:4Y_A : Y_B = 1 : 4YA​:YB​=1:4

and

AA:AB=1:3A_A : A_B = 1 : 3AA​:AB​=1:3
  1. Therefore,
ΔLA:ΔLB=1AAYA:1ABYB=ABYB:AAYA\Delta L_A : \Delta L_B = \frac{1}{A_A Y_A} : \frac{1}{A_B Y_B} = A_B Y_B : A_A Y_AΔLA​:ΔLB​=AA​YA​1​:AB​YB​1​=AB​YB​:AA​YA​

Substitute the ratios:

ΔLA:ΔLB=(3)(4):(1)(1)=12:1\Delta L_A : \Delta L_B = (3)(4) : (1)(1) = 12 : 1ΔLA​:ΔLB​=(3)(4):(1)(1)=12:1
  1. Hence, the elongations in wires A and B are in the ratio
12:1\boxed{12:1}12:1​
  1. Checking options:
  • A: 1:121:121:12 ✗
  • B: 1:361:361:36 ✗
  • C: 12:112:112:1 ✓
  • D: 36:136:136:1 ✗

So the correct option is C.

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