Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 202122 JulyMorning Shift
Exam
JEE Main
Year
2021
Date
22 July
Shift
Morning Shift
Subject
Physics
Chapter
Mechanical Properties of Solids

JEE Main 2021 · 22 July · Morning Shift · Physics · Mechanical Properties of Solids

The area of cross-section of a railway track is 0 . 01 m ^ 2 . The...

The area of cross-section of a railway track is 0.01m2.0 . 01{m}^{2} . The temperature variation is 10°C.10 ° C . Coefficient of linear expansion of material of track is 10−5C−1∘.{10}^{- 5} C - 1 ∘ . The energy stored per meter in the track is Jm−1.J{m}^{- 1} . (Young's modulus of material of track is 1011Nm−2{10}^{11}N{m}^{- 2})

Correct answer

5

Step-by-step solution

Elastic energy =Y2(strain)2×= \dfrac{Y}{2} ( strain{)}^{2} \times Area ×\times length

⇒⇒ Elastic energy per unit length =Y2(strain)2×= \dfrac{Y}{2} ( strain{)}^{2} \times Area

((strain =Δℓℓ=α\DeltaT=10−5×10=10−4)= \dfrac{\Deltaℓ}{ℓ} = \alpha\DeltaT = {10}^{- 5} \times 10 = {10}^{- 4} )
=10112×(10−4)2×10−2=5Jm−1= \dfrac{{10}^{11}}{2} \times {\left({10}^{- 4}\right)}^{2} \times {10}^{- 2} = 5J{m}^{- 1}

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 2026A lift of mass 1600 kg is supported by thick iron wire. If the maximum stress which the… JEE Main 2026The two wires A and B of equal cross-section but of different materials are joined… JEE Main 2026A copper wire of length 3 m is stretched by 3 mm by applying an external force. The… JEE Main 2026The Young's modulus of steel wire of radius r and length L is Y . If the radius r and… JEE Main 2026Two wires as shown in the figure below, made of steel and have breaking stress of 12 ×… JEE Main 2026A cube has side length 5 cm and modulus of rigidity 10^5 N/m ^2 . The displacement… JEE Main 2026A 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