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 ${100}^{0}C$ the length of the gap increase to 1.02 cm.$\alpha$ of material of wire is

• A. $2\times {10}^{-4/0}C$
• B. $4\times {10}^{-4/0}C$
• C. $6\times {10}^{-4/0}C$
• D. $1\times {10}^{-4/0}C$

Answer 1

Answer: (A)

$2\times {10}^{-4/0}C$

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 portion.
So, if $1cm$ becomes $1.02cm,60cm$ will becomes $61.2cm$
So, change in length $=61.2cm-60cm=1.2cm$
original length is $60cm$ and change in temperature $={100}^{o}C$
Putting these values in the formula of $\alpha =\frac{dt}{\times dt},$ where $dl=$ change in length and $dt=$
change in temperature, we get, $\alpha =2\times {10}^{-4}{/}^{o}c$