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An iron tyre is to be fitted onto a wood...

An iron tyre is to be fitted onto a wooden wheel 1.0 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 `3.6xx10^-5//^@C`)

A

`167^(@)C`

B

`334^(@)C`

C

`500^(@)C`

D

`1000^(@)C`

Text Solution

Verified by Experts

The correct Answer is:
C
Initial diameter of tyre = (1000 - 6) mm = 994 mm, so initial radius of tyre `R=(994)/(2)497` mm and change in diameter `DeltaD = 6` mm so `DeltaR = (6)/(2)= 3 `mm
After increasing temperature by `Delta theta` tyre will fit onto wheel
Increment in the length (circumference) of the iron tyre
`DeltaL=L xx alpha xx DeltaT=Lxx(gamma)/(3)xx Delta theta ["As" alpha=(gamma)/(3)]`
`2pi DeltaR=2piR((gamma)/(3))Delta theta`
`rArr Delta theta=(3)/(gamma) (DeltaR)/(R)=(3xx3)/(3.6xx10^(-5)xx497) rArr Delta theta=500^(@)C`
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