Name: Poisson's Ratio
Uploaded: 2019-07-19
Duration: 9 min 46 s
Description: In this video, let us discuss Poisson's ratio, the most interesting and important measure of a property of a material. Watch this to explore.

Question

The area of cross-section of metal rod is

1 {cm}^{2}

. It is clamped tightly at its two ends at

0 ° C

. The rod is heated to

100 ° C

. Calculate the tension produced at its two ends. Coefficient of linear expansion of metal is

1.2 \times 10^{- 5} ° C^{- 1}

and Young's modulus is

2.0 \times 10^{11} N m^{- 2}

.

Accepted Answer

Given:

Area of metal rod $= 1 {cm}^{2} = 1 \times 10^{- 4} m^{2}$

Initial temperature $= 0 ° C$

Final temperature $= 100 ° C$

$(α)$ Coefficient of linear expansion of metal is $1.2 \times 10^{- 5} / ° C^{1}$

$Y = 2.0 \times 10^{11} N / m^{2}$

Tension produced at two ends of rod using the relation $\frac{b}{w}$ change in length of wire and coefficient of linear expression

$∆ L = α L ∆ t$

$L =$ Original length

$∆ L =$ Change in length

$α =$ Coefficient of linear expansion of wire

$∆ t =$ Change in Temperature

$\frac{∆ L}{L} = α ∆ t = s t r a i n$

strain $= 1.2 \times 10^{- 5} ° C^{- 1} \times (100 - 0) ° C$

strain $= 1.2 \times 10^{- 3}$

We know that

$Y = \frac{s t r e s s}{s t r a i n} = \frac{\frac{F}{A}}{s t r a i n} = \frac{T}{A \times s t r a i n}$

$T = Y \times A \times s t r a i n$

$T = 2 \times 10^{11} \times 1 \times 10^{- 4} 1.2 \times 10^{- 3} N$

$T = 2.4 \times 10^{4} N$

Important Questions on Elasticity

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The area of cross-section of metal rod is 1 cm2. It is clamped tightly at its two ends at 0°C. The rod is heated to 100°C. Calculate the tension produced at its two ends. Coefficient of linear expansion of metal is 1.2×10-5°C-1 and Young's modulus is 2.0×1011 N m-2.

Important Questions on Elasticity

Learn and Prepare for any exam you want !