KVPY SX SB Exam 2015 Question Paper

Question : 93 of 120

Marks: +1, -0

A horizontal steel railroad track has a length of 100 m when the temperature is 25ºC. The track is constrained from expanding or bending. The stress on the strack on a hot summer day, when the temperature is 40ºC, is
(Note : the linear coefficient of thermal expansion for steel is 1.1 × 10

^{–5}

/ºC and the Young's modulus of steel is 2 × 10

^{11}

Pa)

6.6 × 10 $^{7}$ Pa
8.8 × 10 $^{7}$ Pa
3.3 × 10 $^{7}$ Pa
5.5 × 10 $^{7}$ Pa

Validate

Solution:

When some body is constrained from expanding or bending then on heating thermal stress get develop in the body.
Stress

= Y∝ ∆T

= 2 × 10^11 × 1.1 × 10^{–5} × (40 -25)

= 3.3 × 10^7

N/m

^{2}

= 3.3 × 10^7

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