1.

A brass rod of length `50 cm` and diameter `3.0 cm` is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at `250^(@)C`, if the original length are at `40.0^(@)C`? (Coefficient of linear expansion of brass `=2.0 xx 10^(-5)//^(@)C, steel = 1.2 xx 10^(-5)//^(@)C`A. `0.27 cm`B. `0.34 cm`C. `0.21 cm`D. `0.18 cm`

Answer» Correct Answer - B
Change in temperature of each rod,
`Delta T = 250 -40 = 210^(@)C`
Clearly change in length of the brass bar
`Delta L_(S)=alpha_(S)Ldelta T = (1.2 xx 10^(-5)) xx 50 xx 210 = 0.126 cm`
Since the ends of the rod are free to expand, change in the length of the combined rod
`Delta L = Delta L_(b) + Delta L_(s) = 0.21 + 0.13 = 0.34 cm`.


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