Sum

**Solve the following problem.**

A blacksmith fixes iron ring on the rim of the wooden wheel of a bullock cart. The diameter of the wooden rim and the iron ring are 1.5 m and 1.47 m respectively at room temperature of 27 °C. To what temperature the iron ring should be heated so that it can fit the rim of the wheel? (α_{iron} = 1.2 × 10^{–5}K^{–1}).

Advertisement Remove all ads

#### Solution

**Given:** d_{w} = 1.5 m, d_{i} = 1.47 m, T_{1} = 27 °C.

α_{i} = 1.2 × 10^{–5}/ K

**To find:** Temperature (T_{2})

**Formula: **α = `("d"_"w" - "d"_"i")/("d"_"i" ("T"_2 - "T"_1))`

**Calculation: **From formula,

`"T"_2 = ("d"_"w" - "d"_"i")/("d"_"i" alpha) + "T"_1`

`= (1.5 - 1.47)/(1.47 xx 1.2 xx 10^-5) + 27`

= 1700.7 + 27

= 1727.7 °C

Iron ring should be heated to temperature of **1727.7 °C**.

Concept: Thermal Expansion

Is there an error in this question or solution?

Advertisement Remove all ads

#### APPEARS IN

Advertisement Remove all ads

Advertisement Remove all ads