Question

An iron ring $1.20m$ in diameter is to be part on a wooden cart a wheel. The diameter of this wheel $1.0cm$ greater than that of the ring. The temperature of the ring that must be raised before it slips the wooden wheel is (Coefficient of linear expansion of iron $=12\times {10}^{-6}{/}^{\circ }C$)

• A. ${600.4}^{\circ }C$
• B. ${694.4}^{\circ }C$
• C. ${294.4}^{\circ }C$
• D. ${300.4}^{\circ }C$

Answer 1

The correct option is B ${694.4}^{\circ }C$

$\begin{array}{cc}\text{Given -}& \text{Diameter of iron ring}=1.20m\\ & \text{Diameter of wooden cart is 1 cm greater}\\ & \text{than the iron ring.}\\ & \text{Coefficient of linear expansion}\alpha =12\times {10}^{-6}/{}^{\circ }C\end{array}$

$\begin{array}{c}\text{For the ring to slip -}\\ \text{Diameter of Ring = Diameter of wooden wheel.}\end{array}$

$\begin{array}{c}\text{we must Increase the Temperature of the Iron Ring}\\ \text{to get an increment of}1cm=0.01m\end{array}$

$\begin{array}{c}\text{we know-}\\ \Delta D=D_0\cdot \alpha \cdot \Delta T\end{array}$

$\begin{array}{c}\Rightarrow 0.01m=1.2\times 12\times {10}^{-6}\times \Delta T\\ \Rightarrow \Delta T=\frac{0.01}{12\times {10}^{-6}\times 1.2}={694.4}^{\circ }C\\ \text{Hence the Temperature must be increased by}{694.4}^{\circ }C\end{array}$