An iron tyre is to be fitted onto a...
Question
An iron tyre is to be fitted onto a wooden wheel 1.0 min diameter. The diameter of the tyre is 6 mm smaller than that of wheel. The tyre should be heated so that its
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An iron tyre is to be fitted onto a wooden wheel ( 1.0 mathrm{m} ) in diameter. The diameter of the tyre is 6 mm smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of (coefficient of volume expansion of iron is ( 3.6 times 10^{-5} /^{circ} mathrm{C} ) )
(1)( quad 167^{circ} mathrm{C} )
(2) ( 334^{circ} mathrm{C} )
(3) ( 500^{circ} mathrm{C} )
(4)( quad 1000^{circ} mathrm{C} )

JEE/Engineering Exams
Physics
Solution
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An iron tyre is to be fitted onto a wooden wheel 1.0 min diameter. The diameter of the tyre is 6 mm smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of (coefficient of volume expansion of iron is 3.6 x 10-51°C)
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Radius(R) of wooden wheel=0.5m
Radius of irm type (R)=0.497m
( Delta D=6 m m )
[
So: quad Delta R=3 m m
]
( as ; quad Delta L=L alpha Delta T )
[
begin{array}{l}
(2 pi Delta R)=(2 pi R)left(frac{1}{3} times 3.6 times 10^{-5}right) times Delta T
2 pi times 0.03=2 pi times 0.497 times frac{1}{3} times 3.6 times 10^{-5} times Delta 7
Rightarrow {triangle T=500^{circ}C}
end{array}
]

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