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. The length of the longer portion of the composite bar in cm at 0° C is

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. The length of the longer portion of the composite bar in cm at 0° C is (A) 23 cm (B) 16 cm (C) 18 cm (D) 20 cm

Tardigrade Admin · Accepted Answer

Using α=(Δ L/L0 ⋅ Δ T) 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

23 cm

16 cm

18 cm

20 cm

Using α=L0​⋅ΔTΔL​ α1​=30×1000.0650​; α2​=30×1000.0350​ L01​⋅α1​⋅ΔT+L02​⋅α2​⋅ΔT =0.0580 and L01​+L02​=30 Solving L01​=23cm

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