Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Heat and Thermodynamics question

2017 · 9 Apr · Shift 1 · Q64
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Heat and Thermodynamics
  5. /2017 · 9 Apr · Shift 1 · Q64

Heat and Thermodynamics question

2017 · 9 Apr · Shift 1 · Q64

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1
A steel rail of length 5 m and area of cross section 40cm2 is prevented from expanding along its length while the temperature rises by 10oC. If coefficient of linear expansion and Young’s modulus of steel are 1.2×10−5 K−1 and 2×1011 Nm−2 respectively, the force developed in the rail is approximately :
  1. A
    2 ×\times× 107 N
  2. B
    1 ×\times× 105 N
  3. C
    2 ×\times× 109 N
  4. D
    3 ×\times× 10 −-− 5 N
View written solutionFree

Correct answer: B

  1. Thermal strain if free to expand

If the rail were free, its thermal strain would be

ϵth=αΔT\epsilon_{\text{th}} = \alpha \Delta Tϵth​=αΔT

where

α=1.2×10−5 K−1,ΔT=10∘C\alpha = 1.2\times 10^{-5}\ \text{K}^{-1}, \quad \Delta T = 10^\circ \text{C}α=1.2×10−5 K−1,ΔT=10∘C

So,

ϵth=1.2×10−5×10=1.2×10−4\epsilon_{\text{th}} = 1.2\times 10^{-5} \times 10 = 1.2\times 10^{-4}ϵth​=1.2×10−5×10=1.2×10−4
  1. Since expansion is prevented

The rail cannot expand, so an equal compressive mechanical strain is produced. Hence the stress developed is

σ=Yϵ=YαΔT\sigma = Y \epsilon = Y\alpha \Delta Tσ=Yϵ=YαΔT

Given

Y=2×1011 N/m2Y = 2\times 10^{11}\ \text{N/m}^2Y=2×1011 N/m2

Thus,

σ=2×1011×1.2×10−4\sigma = 2\times 10^{11} \times 1.2\times 10^{-4}σ=2×1011×1.2×10−4 σ=2.4×107 N/m2\sigma = 2.4\times 10^7\ \text{N/m}^2σ=2.4×107 N/m2
  1. Area of cross section

Given area:

40 cm2=40×10−4 m2=4×10−3 m240\ \text{cm}^2 = 40\times 10^{-4}\ \text{m}^2 = 4\times 10^{-3}\ \text{m}^240 cm2=40×10−4 m2=4×10−3 m2
  1. Force developed

Using

F=σAF = \sigma AF=σA

we get

F=2.4×107×4×10−3F = 2.4\times 10^7 \times 4\times 10^{-3}F=2.4×107×4×10−3 F=9.6×104 NF = 9.6\times 10^4\ \text{N}F=9.6×104 N

This is approximately

1×105 N1\times 10^5\ \text{N}1×105 N
  1. Option check
  • A: 2×107 N2\times 10^7\,\text{N}2×107N ❌
  • B: 1×105 N1\times 10^5\,\text{N}1×105N ✅
  • C: 2×109 N2\times 10^9\,\text{N}2×109N ❌
  • D: 3×10−5 N3\times 10^{-5}\,\text{N}3×10−5N ❌

Therefore, the correct answer is Option B.

PreviousNext

More from Heat and Thermodynamics

  • For the P-V diagram given for an ideal gas, out of the following which one correctly represents the T-P diagram ? Includes diagram2017 · MCQ
  • CP and Cv are specific heats at constant pressure and constant volume respectively. It is observed that CP – Cv = a for hydrogen gas CP – Cv = b for nitrogen gas The correct relation between a and b is2017 · MCQ
  • The temperature of an open room of volume 30 m3 increases from 17oC to 27oC due to the sunshine. The atmospheric pressure in the room remains 1 × 105 Pa. If Ni and Nf are the number of molecules in the room before and after heating,…2017 · MCQ
  • An external pressure P is applied on a cube at 0oC so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and α is its coefficient of linear expansion. Suppose we want to bring the cube to…2017 · MCQ
  • A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75oC. T is given by:…2017 · MCQ
  • A simple pendulum made of a bob of mass m and a metallic wire of negligible mass has time period 2 s at T=0oC. If the temperature of the wire is increased and the corresponding change in its time period is plotted against its temperature,…2016 · MCQ
  • The ratio of work done by an ideal monoatomic gas to the heat supplied to it in an isobaric process is :2016 · MCQ
  • 200 g water is heated from 40oC to 60oC. Ignoring the slight expansion of water, the change in its internal energy is close to (Given specific heat of water = 4184 J/kg/K) :2016 · MCQ