A 30.0 cm long metal rod expands by 0.0650 cm when its temperature is raised from 0° C to 100° C. A second rod of different metal and of the same length expands by 0.0350 cm for the same rise in temperature. A third composite rod, also 30.0 cm long, is made up of pieces of each of the above metals placed end to end and expands by 0.0580 cm when temperature is increased from 0° C to 100° C. Find the length (in cm ) of the smaller portion of the composite rod at 0° C.

Question

A 30.0 cm long metal rod expands by 0.0650 cm when its temperature is raised from 0° C to 100° C. A second rod of different metal and of the same length expands by 0.0350 cm for the same rise in temperature. A third composite rod, also 30.0 cm long, is made up of pieces of each of the above metals placed end to end and expands by 0.0580 cm when temperature is increased from 0° C to 100° C. Find the length (in cm ) of the smaller portion of the composite rod at 0° C. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Using α=(Δ L/L0 ⋅ Δ T), we have α1=(0.0650/30 × 100), α2=(0.0350/30 × 100) L01 ⋅ α1 ⋅ Δ T+L02 ⋅ α2 ⋅ Δ T=0.0580 and L01+L02=30 Solving, L01=23 cm and L02=7 cm.

Using α=L0​⋅ΔTΔL​, we have α1​=30×1000.0650​, α2​=30×1000.0350​ L01​⋅α1​⋅ΔT+L02​⋅α2​⋅ΔT=0.0580 and L01​+L02​=30 Solving, L01​=23cm and L02​=7cm.

Using $α = \frac{Δ L}{L _{0} \cdot Δ T}$ , we have
$α_{1} = \frac{0.0650}{30 \times 100},$
$α_{2} = \frac{0.0350}{30 \times 100}$
$L_{01} \cdot α_{1} \cdot Δ T + L_{02} \cdot α_{2} \cdot Δ T = 0.0580$
and $L_{01} + L_{02} = 30$
Solving, $L_{01} = 23 c m$ and $L_{02} = 7 c m$ .