Question

A rod has a length 2.00000 m at 10.0°C. The length of the rod increases to 2.00060 m
when the temperature increases to 30.0°C. What is the coefficient of lincar expansion
of the material from which the rod is made?
A) 1.0 x 10-5/K
B) 1.5 x 10-5/6
2.5 x 10-5/6
D) 1.0 x 10-3/K
E) 2.0 x 10-57K
​

Answer 1

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Answer 2

Therefore the coefficient of linear expansion of the material is α = 1.5 × 10⁻⁵ / K. ( Option-B )

Given:

Initial Length of the rod = 2 m

Initial Temperature of the rod = 10°C

Final Length of the rod = 2.00060 m

Final Temperature of the rod = 30°C

To Find:

The coefficient of the linear expansion of the material ( α ).

Solution:

The given question be solved very easily as shown below.

Given that,

Initial Length of the rod = L₁ = 2 m

Initial Temperature of the rod = T₁= 10°C

Final Length of the rod = L₂ = 2.00060 m

Final Temperature of the rod = T₂ = 30°C

Change in length = ΔL = L₂ - L₁ = 2.0006 - 2.0000 = 0.0006 m

Change in temperature = ΔT = T₂ - T₁ = 30 - 10 = 20°C

The formula for the coefficient of linear expansion can be given by,

⇒ ΔL = LαΔT

⇒ 0.0006 = 2 × α × 20

⇒ α = 0.0006 / 40 = ( 6/4 ) × 10⁻⁵

⇒ α = 1.5 × 10⁻⁵

Therefore the coefficient of linear expansion of the material is α = 1.5 × 10⁻⁵ / K.

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