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4 years ago

A metal rod 80cm long lengthens by 0.090cm when its temperature rises by 93.6$^o$C. What is the linear expansivity of the metal

Physics

1 answer:

alexandr1967 [171]4 years ago

8 0

Answer: (b)0.000012/k

Explanation:

The linear expansion of the metal rod is given by

$\Delta L= L_0 \alpha \Delta T$

where

$\Delta L=0.090 cm$ is the linear expansion

$L_0 = 80 cm$ is the initial length of the rod

$\alpha$ is the linear expansivity

$\Delta T=93.6^{\circ}C=93.6 K$ is the increase in temperature

By re-arranging the equation, we find the linear expansivity:

$\alpha = \frac{\Delta L}{L_0 \Delta T}=\frac{0.090 cm}{(80 cm)(93.6K)}=0.000012 K^{-1}$

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First, look at the picture to understand the problem before to solve it.

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Here, the point is located in the surface of the cilinder. Therefore, we have to consider the current density of the conductor to calculate the magnetic field as follows:

J: current density

c: outer radius

b: inner radius

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$J= \frac {-I_{c}}{\pi(c^{2}-b^{2} ) }}$

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