Question

An iron tyre is to be fitted on to a wooden wheel 1 m in diameter. The diameter of tyre is 6mm smaller than that of the wheel.The tyre should be heated so that its temperature increases by a minimum of (the coefficient of cubical expansion of iron is $3.6\times {10}^{-5}{/}^{0}C$)

• A. ${167}^{0}C$
• B. ${334}^{0}C$
• C. ${500}^{0}C$
• D. ${1000}^{0}C$

Answer 1

The correct option is C ${500}^{0}C$

The diameter of $\left(d\right)$ of iron tyre should be equal to $\perp m$ i.e., $1000mm$

The initial diameter $\left(d\right)$ of iron tyre

$=1m-6mm$

$=(1000-6)mm$

$=994mm$

we have

cubical expressin $\left(\overline{r}\right)=3.6\times {10}^{-5}{/}^{o}C$

$\Rightarrow 3\alpha =3.6\times {10}^{-5}$

$\Rightarrow \alpha =1.2\times {10}^{-5}{/}^{o}C$

where

$\alpha \to$linear expression

Now, we know that

$l=l_0(\perp +\alpha \Delta \theta )$

there,

$d=d_0(\perp +\alpha \Delta \theta )$

$1000=994(\perp +1.2+{10}^{-5}\Delta \theta )$

$\Rightarrow 994\times 1.2\times {10}^{-5}\Delta \theta =6$

$\Rightarrow \Delta \theta =\frac{6}{994\times 1.2}\times {10}^5={503}^{o}C$

$\Rightarrow \Delta \theta \cong {500}^{o}C$