A blacksmith fixes iron ring on the rim of the wooden wheel of a bullo

1.	A blacksmith fixes iron ring on the rim of the wooden wheel of a bullock cart. The diameter of the rim and the iron ring are 5.243 m and 5.231 m respectively at 27°C. To what temperature should the ring be heated so as to fit the rim of the wheel ?
Answer» Given, T = 27°C, L_T1 = 5.231 m L_T2 = 5.243 m So, L_T2 = L_T1 [1 + α₁ (T₂ - T₁)] ⇒ 5.243 = 5.231 [1 + 1.20 x 10^-5°C^-1 (T₂ - 27°C)] or, T₂ = 218°C

A blacksmith fixes iron ring on the rim of the wooden wheel of a bullock cart. The diameter of the rim and the iron ring are 5.243 m and 5.231 m respectively at 27°C. To what temperature should the ring be heated so as to fit the rim of the wheel ?

Answer»

Given,

T = 27°C, L_T1 = 5.231 m

L_T2 = 5.243 m

So, L_T2 = L_T1 [1 + α₁ (T₂ - T₁)]

⇒ 5.243 = 5.231 [1 + 1.20 x 10^-5°C^-1 (T₂ - 27°C)]

or, T₂ = 218°C