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Question

Two identical square rods of metal are welded end to end as shown in figure (a), 20 calories of heat flows through it in 4 minutes. If the rods are welded as shown in figure (b), the same amount of heat will flow through the rods in

A
1 minute
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B
2 minutes
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C
4 minutes
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D
16 minutes
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Solution

The correct option is A 1 minute
Let K be the thermal conductivity of each rod.
From conduction law,
Qt=KeqA(θ1θ2)L
where,
Keq= equivalent thermal conductivity
A= cross section area of rods
For fig. (a):
Keq = Harmonic mean of K1 & K2
1Keq=K1+K22K1K2=1K
Keq=K
for fig. (b):
Keq=KA+KAA+A=K
(AM of K1 & K2)
Q1=Q2
K(A)2l(θ1θ2)t1=K(2A)l(θ1θ2)t2
Given, t1=4 min & (θ1θ2)=100C
t2=t14=1 min
Hence, option (a) is the correct answer.

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