If two rods of length L and 3 L having coefficient of expansion - and 4 - respectively are connected- average coefficient of linear expansion equals to-A- 5 -4B- 14-13 -D- 18 -18-5

The correct option is C 13 α/4l = l_1 + l_2 (l_1 + l_2) α_ag t = l_1 α_1 t + l_2 α_2 t α_ag = l_1α_1 + l_2α_2/l_1 + l_2 = L(α )+3L(4α )/L + 3L = 13Lα/4L ...

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Byju's Answer

Standard XII

Physics

Thermal Expansion

If two rods o...

Question

If two rods of length L and 3L having coefficient of expansion $α$ and $4 α$ respectively are connected, average coefficient of linear expansion equals to:

\frac{5 α}{4}

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\frac{16 α}{7}

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\frac{13 α}{4}

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\frac{18 α}{5}

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Solution

The correct option is C $\frac{13 α}{4}$
$△ l = △ l_{1} + △ l_{2}$
$(l_{1} + l_{2}) α_{a g} △ t = l_{1} α_{1} △ t + l_{2} α_{2} △ t$

$α_{a g} = \frac{l_{1} α_{1} + l_{2} α_{2}}{l_{1} + l_{2}} = \frac{L (α) + 3 L (4 α)}{L + 3 L}$

$= \frac{13 L α}{4 L} = \frac{13 α}{4}$

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If two rods of length L and 3L having coefficient of expansion α and 4α respectively are connected, average coefficient of linear expansion equals to:

The correct option is C 13α4△l=△l1+△l2 (l1+l2)αag△t=l1α1△t+l2α2△t αag=l1α1+l2α2l1+l2=L(α)+3L(4α)L+3L =13Lα4L=13α4

If two rods of length L and 3L having coefficient of expansion $α$ and $4 α$ respectively are connected, average coefficient of linear expansion equals to:

The correct option is C $\frac{13 α}{4}$
$△ l = △ l_{1} + △ l_{2}$
$(l_{1} + l_{2}) α_{a g} △ t = l_{1} α_{1} △ t + l_{2} α_{2} △ t$

$α_{a g} = \frac{l_{1} α_{1} + l_{2} α_{2}}{l_{1} + l_{2}} = \frac{L (α) + 3 L (4 α)}{L + 3 L}$

$= \frac{13 L α}{4 L} = \frac{13 α}{4}$