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Two rods of equal length 60 cm each are joined together end to end. The coefficients of linear expansion are $24\times10^{-6\circ}C^{-1}$ and $1.2\times10^{-5\circ}C^{-1}$. Initial temperature $30^{\circ}C$ is increased to $100^{\circ}C$. Find final length (in cm).
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MEDIUM
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Q: Two rods of equal length 60 cm each are joined together end to end. The coefficients of linear expansion are $24\times10^{-6\circ}C^{-1}$ and $1.2\times10^{-5\circ}C^{-1}$. Initial temperature $30^{\circ}C$ is increased to $100^{\circ}C$. Find final length (in cm).

Question Analysis & Solution

Step-by-Step Solution

  1. Step 1: Calculate the change in temperature.

    ΔT = Final temperature - Initial temperature = 100°C - 30°C = 70°C

  2. Step 2: Calculate the change in length for the first rod.

    ΔL1 = L1 * α1 * ΔT = 60 cm * (24 × 10-6 °C-1) * 70°C = 0.1008 cm

  3. Step 3: Calculate the change in length for the second rod.

    ΔL2 = L2 * α2 * ΔT = 60 cm * (1.2 × 10-5 °C-1) * 70°C = 0.0504 cm

  4. Step 4: Calculate the total change in length.

    ΔLtotal = ΔL1 + ΔL2 = 0.1008 cm + 0.0504 cm = 0.1512 cm

  5. Step 5: Calculate the final length.

    Final Length = Initial Length + Total Change in Length = (60 cm + 60 cm) + 0.1512 cm = 120 cm + 0.1512 cm = 120.1512 cm

Correct Answer: 120.1512

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