Question

On a hot day where the temperature is 32 deg celsius, the distance between two lamp post on the road is 30m as measured by a metal tape whose coefficient of linear expansion is hypothetically (50 x 10^-6)/deg celsius. If the tape gives its correct reading at 20 deg celsius, what is the actual distance between the lamp posts?

Answer 1

grabbed this from Wiki

\(\dfrac{\Delta L}{L} = \alpha\Delta T\)

and you know that \(\Delta L + L = 30 = L(\alpha \Delta T + 1 ) \)

solve for L

with \(\alpha = 50 \times 10^{-6}\) deg celsius

and \(\Delta T = 12\)

Answer 2

We can solve it in little different way

Answer 3

We know the equation
L=L0(1+alpha*theta)

Answer 4

If L=30m then
Theta=32°c

Answer 5

Then the equation will b
30=L0(1+50*10^-6*32)

Answer 6

We will get another equation for 20°c

Answer 7

L=L0(1+50*10^-6*20)

Answer 8

Then divide equation 2 by equation 1

Answer 9

L=?