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`)

Options

A. `167^(@)C`
B. `334^(@)C`
C. `500^(@)C`
D. `-1000^(@)C`

Answer

C

Explanation

`d theta=d theta_(0)(1+alpha Delta theta)`
`1000=(1000-6)(1+(gamma)/(3)Delta theta)`
`(gamma)/(3)Delta theta=(1000)/(994)-1=(6)/(994)`
`(3.6xx10^(-5))Delta theta=(6xx3)/(994)`
`Delta theta=503^(@)C=500^(@)C`