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Question
An iron ring measuring 15.00 cm in diameter is to be shrunk on a pulley which is 15.05 cm in diameter. All measurements are done at a room temperature of 20∘C. To what minimum temperature should the ring be heated to make the job possible? Calculate the strain developed in the ring when it comes to the room temperature. Coefficient of linear expansion of iron = 12 × 10−6/∘C.
An iron ring measuring 15.00 cm in diameter is to be shrunk on a pulley which is 15.05 cm in diameter. All measurements are done at a room temperature of 20∘C. To what minimum temperature should the ring be heated to make the job possible? Calculate the strain developed in the ring when it comes to the room temperature. Coefficient of linear expansion of iron = 12 × 10−6/∘C.
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Solution
The correct option is A
The ring should be heated to increase its diameter from 15.00 cm to 15.05 cm.
Using,
l2 = l1(1+aΔθ)
⇒ Δθ = 0.05 cm15.00 cm × 12 × 10−6/∘C
⇒ Δθ = 278∘C.
The temperature = 20∘C + 278∘C = 298∘C.
Therefore, the strain developed = l2−l1l1 = 3.33 × 10−3.
The ring should be heated to increase its diameter from 15.00 cm to 15.05 cm.
Using,
l2 = l1(1+aΔθ)
⇒ Δθ = 0.05 cm15.00 cm × 12 × 10−6/∘C
⇒ Δθ = 278∘C.
The temperature = 20∘C + 278∘C = 298∘C.
Therefore, the strain developed = l2−l1l1 = 3.33 × 10−3.
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