    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 minuteLet K be the thermal conductivity of each rod. From conduction law, Qt=KeqA(θ1−θ2)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(θ1−θ2)t1=K(2A)l(θ1−θ2)t2 Given, t1=4 min & (θ1−θ2)=100∘C ⇒t2=t14=1 min Hence, option (a) is the correct answer.  Suggest Corrections  2      Explore more