Question

A brass rod and lead rod each 80 cm long at 0⁰C 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

$(\alpha_{brass} = 18 \times 10^{- 6} ⥂ /{^\circ}C\text{ and }\alpha_{lead} = 28 \times 10^{- 6} ⥂ /{^\circ}C)$

• A. 0.2 mm
• B. 0.8 mm
• C. 1.4 mm
• D. 1.6 mm

Answer 1

Answer: (B)

0.8 mm

Answer 2

The Brass rod and the lead rod will suffer expansion when placed in steam bath.

∴ Length of brass rod at 100⁰C

$L_{brass}^{'} = L_{brass}(1 + \alpha_{brass}\Delta T)$ = $80\lbrack 1 + 18 \times 10^{- 6} \times 100\rbrack$

and the length of lead rod at 100⁰C

$L_{lead}^{'} = L_{lead}(1 + \alpha_{lead}\Delta T)$ = $80\lbrack 1 + 28 \times 10^{- 6} \times 100\rbrack$

Separation of free ends of the rods after heating =

$L_{lead}^{'} - L_{brass}^{'}$=$80\lbrack 28 - 18\rbrack \times 10^{- 4} = 8 \times 10^{- 2}cm = 0.8mm$