Question

A brass scale is graduated at 10°C. What
is the true length of a zinc rod which
measures 60.00cm on this scale at
30°C ? Coefficient of linear expansion of
brass = 18 x 10-6K-1​

Answer 1

Given that,

Increases temperature = 10°C

Measured length L'= 60.00 cm

Initial temperature = 30°C

We need to calculate the true length of a zinc rod

Using formula of true length

$L=L'(1+\alpha\Delta T)$

Where, L'= given length

$\alpha$ = Coefficient of linear expansion of  brass

$\Delta T$ = change in temperature

Put the value into the formula

$L=60(1+18\times10^{-6}\times(30-10))$

$L=60(1+0.00036)$

$L=60.02\ cm$

Hence, The true length of a zinc rod is 60.02 cm.

Answer 2

Given that,

Increases temperature = 10°C

Measured length L'= 60.00 cm

Initial temperature = 30°C

We need to calculate the true length of a zinc rod

Using formula of true length

$L=L'(1+\alpha\Delta T)$

Where, L'= given length

$\alpha$ = Coefficient of linear expansion of  brass

$\Delta T$ = change in temperature

Put the value into the formula

$L=60(1+18\times10^{-6}\times(30-10))$

$L=60(1+0.00036)$

$L=60.02\ cm$

Hence, The true length of a zinc rod is 60.02 cm.

✔️✔️✔️