If two rods of length L and 2L having coefficients of linear expansion α and 2α respectively are c

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10-1.Thermometry, Thermal Expansion and Calorimetry

normal

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 linear expansion of the composition rod equals:

$\frac{3}{2}\alpha $

$\frac{5}{2}\alpha $

$\frac{5}{3}\alpha $

none of these

Initial length of combination is $L+2 L=3 L$

Increment in first rod is $L \alpha \Delta t$

Increment in second rod is $(2 L)(2 \alpha) \Delta t=4 L \alpha \Delta t$

So increment in combination is sum of both so $5 L \alpha \Delta t$

Initial length of combination was $3 L$ so coefficient for combination is

$\frac {change}{initial \,length \times change\, in \,temperature}$

$=\frac{5 L \alpha \Delta t}{3 L \Delta t}=5 \alpha / 3$

Standard 11

Physics

normal

medium

easy

medium

medium