Properties Of Solids And Liquids Question 426
Question: An iron tyre is to be fitted on to a wooden wheel 1m in diameter. The diameter of tyre is 6 mm smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of (the coefficient of cubical expansion of iron is$ 3.6\times {{10}^{-5}}/{}^\circ C $ )
Options:
A) $ 167{}^\circ C $
B) $ 334{}^\circ C $
C) $ 500{}^\circ C $
D) $ 1000{}^\circ C $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] Initial diameter of tyre =(1000- 6) mm = 994 mm,
so initial radius of tyre $ R=\frac{994}{2}=497mm $
and change in diameter AD = 6 mm so $ \Delta R=\frac{6}{2} = 3 mm $ .
After increasing temperature by $ \Delta \theta $ tyre will fit onto wheel Increment in the length (circumference) of the iron tyre $ \Delta L=L\times \alpha \times \Delta \theta =L\times \frac{\gamma }{3}\times \Delta \theta $
$ [As\alpha =\frac{\gamma }{3}] $
$ 2\pi \Delta R=2\pi R( \frac{\gamma }{3} )\Delta \theta \Rightarrow \Delta \theta $
$ =\frac{3}{\gamma }\frac{\Delta R}{R}=\frac{3\times 3}{3.6\times {{10}^{-5}}\times 497}\Rightarrow \Delta \theta \simeq {{500}^{\circ }}C $
