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JEE Main
Exam
JEE Main
Subject
Physics
Chapter
Mechanical Properties of Solids

JEE Main · Physics · Mechanical Properties of Solids

A wire of initial length L and raidus r is stretched by a length l...

A wire of initial length LL and raidus rr is stretched by a length ll. Another wire of same material but with initial length 2L2 L and radius 2r2 r is stretched by a length 2l2 l. The ratio of stored elastic energy per unit volume in the first and second wire is

Options

  1. A1:41: 4
  2. B1:21: 2
  3. C2:12: 1
  4. D1:11: 1

Correct answer

D. 1:11: 1

Step-by-step solution

Elastic energy per unit volume of wire. μ=12×\mu=\frac{1}{2} \times Young's modulus ×( Strain )2∴u1u2={( Strain )1( Strain )2}2=l2L2×4L24l2=1:1\times(\text { Strain })^{2}\therefore \quad \frac{u_{1}}{u_{2}}=\left\{\frac{(\text { Strain })_{1}}{(\text { Strain })_{2}}\right\}^{2}=\frac{l^{2}}{L^{2}} \times \frac{4 L^{2}}{4 l^{2}}=1: 1
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