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A metal rod is fixed rigidly at two end...

A metal rod is fixed rigidly at two ends so as to prevent its thermal expansion. If L, `alpha` and Y respectively denote the length of the rod, coefficient of linear thermal expansion and Young's modulus of its material, then for an increase in temperature of the rod by `DeltaT`, the longitudinal stress developed in the rod is

A

inverse proportional to `alpha`

B

inversely proportional to Y

C

directly proportional to `(DeltaT)/Y`

D

independent of L

Text Solution

Verified by Experts

The correct Answer is:
D
Longitudinal thermal stress `=YalphaDeltaT`.
The option (D) is correct.
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Knowledge Check

  • A uniform rod weights W, has length L and cross sectional area a. The rod is suspended from one of its ends. The young's modulus of its material is Y. Increase in length of the rod will be

    A
    zero
    B
    `(WL)/(2aY)`
    C
    `(WL)/(aY)`
    D
    `(2WL)/(aY)`

  • The ratio of the lengths of two metallic rods is 2:3 and the ratio of the coefficients of linear expansion of their materials is 4:3. The ratio of their linear expanions for the same rise in temperature is

    A
    `1:2`
    B
    `2:3`
    C
    `3:4`
    D
    `8:9`

  • The stress along the length of a rod (with rectangular cross section) is 1% of the Young's modulus of its material. What is the approximate percentage of change of its volume ? (Poisson's ratio of the material of the rod is 0.3)

    A
    0.03
    B
    0.01
    C
    `0.7%`
    D
    `0.4%`

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