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Question

A brass rod and lead rod each 80 cm long at 0C are clamped together at one end with their free ends coinciding. The separation of free ends of the rods if the system is placed in a steam bath is (αbrass=18×106/Candαlead=28×106/C)

A
0.2 mm
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B
0.8 mm
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C
1.4 mm
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D
1.6 mm
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Solution

The correct option is B 0.8 mm
The Brass rod and the lead rod will suffer expansion when placed in steam bath.
Length of brass rod at 100C Lbrass=Lbrass(1+αbrassΔT) = 80[1+18×106×100]
and the length of lead rod at 100CLlead=Llead(1+αleadΔT) = 80[1+28×106×100]
Separation of free ends of the rods after heating = LleadLbrass=80[2818]×104=8×102cm=0.8mm

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