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Question

Two identical rods AB and CD are connected across the end points of a diameter of a ring as shown in the figure. Radius of ring is equal to length of rod AB (of CD) and area of cross-section is same everywhere in the assembly. Rods and ring also have same material. If point A maintained at 100oC and point D is maintained at 0oC, then temperature of point C will be
1078894_3f6c2626dfe94fec9f117fbc55cf4ce6.png

A
62oC
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B
37oC
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C
28oC
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D
45oC
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Solution

The correct option is C 28oC

Given that,

Point A maintained =1000C

Point D maintained =00C

Now, according to figure

k(100θB)al=2k(θBθC)aπl=k(θC0)al

100θB=2π(θBθC)=θC

2θB2θC=πθC

θB=(π+22)θC=θC

100=[1+(π+22)]θC

100=π+42×θC

θC=200π+4

θC=28.01

θC=280

Hence, the temperature of point C will be 280


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