Question

A brass rod and lead rod each 80 cm long at $0^{\circ }C$ 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 $({\alpha }_{brass}=18\times {10}^{-6}{/}^{\circ }Cand{\alpha }_{lead}=28\times {10}^{-6}{/}^{\circ }C)$

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

Answer 1

The correct option is B 0.8 mm

The Brass rod and the lead rod will suffer expansion when placed in steam bath.
$\therefore$ Length of brass rod at ${100}^{\circ }C$ $L_{brass}^{\prime }=L_{brass}(1+{\alpha }_{brass}\Delta T)$ = $80[1+18\times {10}^{-6}\times 100]$
and the length of lead rod at ${100}^{\circ }C{L}_{lead}^{\prime }=L_{lead}(1+{\alpha }_{lead}\Delta T)$ = $80[1+28\times {10}^{-6}\times 100]$
Separation of free ends of the rods after heating = $L_{lead}^{\prime }-L_{brass}^{\prime }$=$80[28-18]\times {10}^{-4}$$=8\times {10}^{-2}cm=0.8mm$