Question

An aluminium bar of 8 m length and a steel bar of 5 mm longer in length are kept at ${30}^{\circ }C$. If the ambient temperature is raised gradually, at what temperature the aluminium bar coil elongate 5 mm longer than steel bar (the linear expansion coefficients for steel and aluminium are $12\times {10}^{-6}\circ /Cand23\times {10}^{-6}\circ /C$ respectively ) .

• A. ${50.7}^{\circ }C$
• B. ${69.0}^{\circ }C$
• C. ${143.7}^{\circ }C$
• D. ${33.7}^{\circ }C$

Answer 1

The correct option is C ${143.7}^{\circ }C$


$\therefore$ Final elongation of ;A 1 ' is 10 mm more than steel

$\uparrow t=(T-3b)$

$\Rightarrow (l\alpha t{)}_{al}-(l\alpha t{)}_{steel}=10$

$(T-30)(23\times {10}^{-6}\times 8000-12\times {10}^{-6}\times 8005)=10$

$T={143.7}^{\circ }C$