Question

A wire of length 60 cm. Is bent into a circle with a gap of 1 cm. At its ends. On heating it by $100^{\circ} C$, the length of the gap increases to 1 .02 cm, $\alpha$ of material of wire is

• A. $2\times 10^{-4} /^{\circ} C$
• B. $4\times 10^{-4} /^{\circ} C$
• C. $6\times 10^{-4} /^{\circ} C$
• D. $1\times 10^{-4} /^{\circ} C$

Answer 1

Answer: (A)

Since on heating the length of the wire increases, it expands outwards, making the size of the ring bigger. consequently, the gap in the ring also becomes bigger in the same proportion.
So, if $1 cm$ become $1.02 cm , 60 cm$ will become $61.2 cm$
So, change in length $=61.2 cm -60 cm =1.2 cm$
original length is $60 cm$ and change in temperature $=100^{\circ} C$
Putting these values in the formula of $\alpha=\frac{ dl }{ lxdt }$, where $dl =$ Change in length and $dt =$ change in temperature, we get, $\alpha=2 \times 10^{-4} /{ }^{\circ} C$