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  • A non isotropic solid metal cube has coefficients of linear expansion as  along the x-axis and <img alt="5\times 10^{-6}

A non isotropic solid metal cube has coefficients of linear expansion as 5\times 10^{-5} /^oC along the x-axis and 5\times 10^{-6} /^oC along the y-axis and z-axis. If the coefficient of volume expansion of the solid is C\times 10^{-6} /^oC, then the value of C is:-        
Option: 1 60
Option: 2 40
Option: 3 75
Option: 4 100

Answers (1)

best_answer

 

 

Thermal Expansion and its types -

Let the length of cube be L.

Given,\alpha_x=5\times 10^{-5} /^oC and \alpha_y=5\times 10^{-6} /^oC=\alpha_z

Let the coefficient of volume expansion be \gamma

After increase in temperature:-

Increase in volume of cube=L^3\times\gamma------------(1)

and we can also write it as:- L(1+\alpha_x)\timesL(1+\alpha_y)\timesL(1+\alpha_z)------------(2)\

from equation 1 and 2 we get:-

\gamma L^3=L^3(1+\alpha_x)(1+\alpha_y)(1+\alpha_z)

\Rightarrow \gamma =(\alpha_x+\alpha_y+\alpha_z)\ by \ ignoring \ \alpha_x\alpha_y, \ \alpha_x\alpha_z, \ \alpha_y\alpha_z, and \ \alpha_x\alpha_y\alpha_z

\Rightarrow \gamma =(5\times10^{-5}+5\times10^{-6}+5\times10^{-6})

\Rightarrow \gamma=6\times10^{-5}/^oC

From question:- \gamma=C\times 10^{-6} /^oC

So, C=60

SO the correct answer is option 1.

Posted by

Ritika Jonwal

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