When a rod is heated but prevented from expanding, the stress developed is indep

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When a rod is heated but prevented from expanding, the stress developed is independent of

Options:

A . material of the rod

B . rise in temperature

C . length of rod

D . none of these

Answer: Option C
:
C

L_{t} = L_{0} (1 + α △ θ)

△ L = L_{t} - L_{0} = L_{0} α △ θ

If the same rod of lenghth

L_{0}

is subjected to stress along its length, then extension in length can be calculated by Hooke's law

Y = \frac{s t r e s s}{s t r a i n} = \frac{s t r e s s}{\frac{△ L}{L_{n}}}

= \frac{L_{0} \times s t r e s s}{△ L}

Therefore

△ L = \frac{L_{0} \times s t r e s s}{Y}

If the rod is prevented from expanding, we have

L_{o} α △ θ = \frac{L_{o} \times s t r e s s}{Y}

Therefore stress

= Y α △ θ

= (independent of

L_{0})

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