An iron ring measuring $15.00 c m$ in diameter is to be shrunk on a pulley which is $15.05 c m$ in diameter. All measurements are done at a room temperature of $20^{\circ} C$ . 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 = $12 \times 10^{- 6} /^{\circ} C$ .

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3.33 × 10³

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3.33 × 10^-4

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3.33 × 10^-5

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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,

$l_{2}$ = $l_{1}$ $(1 + a Δ θ)$

$\Rightarrow Δ θ$ = $\frac{0.05 c m}{15.00 c m \times 12 \times 10^{- 6} /^{\circ} C}$

$\Rightarrow Δ θ$ = $278^{\circ} C$ .

The temperature = $20^{\circ} C + 278^{\circ} C$ = $298^{\circ} C$ .

Therefore, the strain developed = $\frac{l_{2} - l_{1}}{l_{1}}$ = $3.33 \times 10^{- 3}$ .

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Similar questions

Q. An iron ring measuring

15.00 c m

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15.05 c m

in diameter. All measurements refer to the room temperature

20^{\circ} 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 \times 10^{- 6} /^{\circ} C

Q. 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 refer to the room temperature

20^{\circ}

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 room temperature.

α

for iron =

12 \times 10^{- 6} /^{\circ}

An iron ring measuring $15.00 c m$ in diameter is to be shrunk on a pulley which is $15.05 c m$ in diameter. All measurements are done at a room temperature of $20^{\circ} C$ . 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 = $12 \times 10^{- 6} /^{\circ} C$ .

Q. An iron ring measuring 15.00 cm in diameter is to be shrink on a pulley which is 15.05 cm in diameter. All measurements refer to the room temperature

20^{\circ}

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 room temperature.

α

for iron =

12 \times 10^{- 6} /^{\circ}

Q. 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 refer to the room temperature

20^{\circ}

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 room temperature.

α

for iron =

12 \times 10^{- 6} /^{\circ}

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