Question

*23. An iron ring 1.20 m in diameter is to be put on
a wooden cart wheel. The diameter of this wheel
is 1.0 cm greater than that of the ring. The
temperature of the ring that must be raised
before it slips on the wooden wheel is (Coefficient
of linear expansion of iron 12 x 10-6/°C).​

Answer 1

The temperature of the ring must be raised before it slips on the wooden wheel is 694.4°C

diameter of iron ring, D = 1.20m

diameter of wooden cart wheel, D' = 1.21 m [as 1cm greater of the ring ]

coefficient of linear expansion of iron, α = 12 × 10^-6 /°C

using concept of linear expansion,

D' = D[1 + α∆T]

⇒1.21 = 1.20 [1 + 12 × 10^-6∆T]

⇒0.01 = 1.2 × 12 × 10^-6∆T

⇒10⁴/14.4 = ∆T

⇒∆T = 694.4°C

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Answer 2

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diameter of iron ring, D = 1.20m

diameter of wooden cart wheel, D' = 1.21 m [as 1cm greater of the ring ]

coefficient of linear expansion of iron, α = 12 × 10^-6 /°C

using concept of linear expansion,

D' = D[1 + α∆T]

⇒1.21 = 1.20 [1 + 12 × 10^-6∆T]

⇒0.01 = 1.2 × 12 × 10^-6∆T

⇒10⁴/14.4 = ∆T

⇒∆T = 694.4°C