Question

A rod of length 40 cm has the coefficient of linear expansion au = 6 x 10" PC. The other rod has coefficient of linear expansion ay = 4 x 10- /"C. If the difference in their length at all Temperature remains the same, the length of the other rod is​

Answer 1

Answer:

60 cm.

Explanation:

1st. rod Δl1 = ∝1l1ΔT1 = 240x10∧-6ΔT

2nd. rod Δl2 = ∝2l2ΔT2 = 4l2x10∧-6ΔT

l2 = 240/4 = 60 cm.

Answer 2

The length of other rod is 60 cm.

Explanation:

Given that,

Length of first rod = 40 cm

Linear expansion of first rod $\alpha=6\times10^{-6}^{\circ}/C$

Linear expansion of other rod $\alpha=4\times10^{-6}^{\circ}/C$

If the difference in their length at all Temperature remains the same.

We need to calculate the length of other rod

Using formula of length

$\Delta L=L\times\alpha\times\Delta T$

Put the value into the formula

For first rod,

$\Delta L=40\times6\times10^{-6}\times\Delta T$....(I)

For other rod,

$\Delta L=L\times4\times10^{-6}\times\Delta T$....(II)

Divided equation (II) by equation (I)

$\dfrac{\Delta L}{\Delta L}=\dfrac{L\times4\times10^{-6}}{40\times6\times10^{-6}}$

$40\times6\times10^{-6}=L\times4\times10^{-6}$

$L=\dfrac{40\times6\times10^{-6}}{4\times10^{-6}}$

$L=60\ cm$

Hence, The length of other rod is 60 cm.

Learn more :

Topic : linear expansion

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