Question

If two rods of length $$L$$ and $$2L$$ having coefficients of linear expansion $$\alpha$$ and $$2\alpha$$ respectively are connected so that total length becomes $$3L$$, the average coefficient of liner expansion of the composition rod equals:

A
32α
B
52α
C
53α
D
none of these

Solution

The correct option is C $$\dfrac {5}{3}\alpha$$Initial length of combination is $$L +2L=3L$$Increment in first rod is $$L\alpha \Delta t$$Increment in second rod is $$(2L) (2\alpha ) \Delta t=4L\alpha \Delta t$$So increment in combination is sum of both so $$5L\alpha \Delta t$$Initial length of combination was $$3L$$ so coefficient for combination is $$\dfrac{change}{\text{initial length* change in temperature}}$$$$=\dfrac{5L\alpha \Delta t}{3L \Delta t }=5\alpha/3$$Option C is correct.Physics

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