Answer to Question #140390 in Mechanics | Relativity for Sabbu Sharma

Question

A steel rod when measured with a zin scale both being at 25 degree C appear to be 1m long. If the zinc scale is correct at 0 degree C, what is the actual length of the rod at 25 degree C ? What will be the length of rod at 0 degree C ?

Answer 1

Solution

Asumption

$\alpha_z=26\times10^{-6}/°C$

$\alpha_s=11\times10^{-6}/°C$

So length of scale at 25°C

$100=l_0(1+\alpha_z\Delta t)$

$l_0=99.93cm$

So

$\Delta l_Z=99.93\times10^{-6}\times26\times25$

$\Delta l_Z=0.064cm$

So lenght of rod at 25°c is

$l_{rod}$ At 25°C =100.064cm

Actual lenght of rod is

$l_{rod \space (measured) }=l_{actual}(1+((\alpha_{Zn}-\alpha_{rod})\Delta t)$

$l_{actual}=\frac{100}{(1+15\times 10^{-6}\times25)}$

$l_{actual}=99.96cm$