Properties Of Solids And Liquids Question 97
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 × 10-5/ºC) [CPMT 1989]
Options:
A) 167ºC
B) 334ºC
C) 500ºC
D) 1000ºC
Show Answer
Answer:
Correct Answer: C
Solution:
Initial diameter of tyre = (1000 - 6) mm = 994 mm,
so initial radius of tyre $ R=\frac{994}{2}=497mm $ and change in diameter DD = 6 mm so $ \Delta R=\frac{6}{2}=3mm $
After increasing temperature by Dq tyre will fit onto wheel Increment in the length (circumference) of the iron tyre DL = L ´ a ´ Dq $ =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 $
therefore $ \Delta \theta =\frac{3}{\gamma }\frac{\Delta R}{R}=\frac{3\times 3}{3.6\times {{10}^{-5}}\times 497} $
therefore $ \Delta \theta =500^{o}C $
