Properties of Matter 1 Question 7

7. A rod of length L at room temperature and uniform area of cross-section A, is made of a metal having coefficient of linear expansion α/C. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when its temperature rises by ΔTK. Young’s modulus, Y for this metal is

(a) F2AαΔT

(b) FAα(ΔT273)

(c) 2FAαΔT

(d) FAαΔT

(2019 Main, 9 Jan I)

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Answer:

Correct Answer: 7. (a)

Solution:

  1. If a rod of length L and coefficient of linear expansion α/C, then with the rise in temperature by ΔTK, its change in length is given as,

ΔL=LαΔTΔLL=αΔT

Also, when a rod is subjected to some compressive force (F), then its’ Young’s modulus is given as

Y= Stress  Strain =FAΔLLΔLL=FYA

Since, it is given that the length of the rod does not change. So, from Eqs. (i) and (ii), we get

αΔT=FYAY=FAαΔT



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