Question # 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} ) )

# 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} )

Solution

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}

]