A steel scale is correct at , the length of a brass tube measured by it at is The correct length of the tube at is (Coefficients of linear expansion of steel and brass are and respectively

Physics · Heat, temperature, thermal expansion, specific heat capacity, calorimetry, change of state, latent heat

A steel scale is correct at , the length of a brass tube measured by it at is Th

A steel scale is correct at \( 0^{\circ} \mathrm{C} \), the length of a brass tube measured by it at \( 40^{\circ} \mathrm{C} \) is \( 5 \mathrm{m} . \) The correct length of the tube at \( 0^{\circ} \mathrm{C} \) is (Coefficients of linear expansion of steel and brass are \( 11 \times \) \( \mathbf{1 0}^{-\mathbf{6} /^{\circ} C} \) and \( \mathbf{1 9} \times \mathbf{1 0}^{-\mathbf{6} /^{\circ} \mathbf{C}} \) respectively

A. \( 4.001 \mathrm{m} \)
B. \( 5.001 m \)
C. 4 .999 m \)
D. \( 4.501 m \)

Step-by-step solution

The steel scale is correct at 0°C, so at 40°C its markings are expanded. The actual length of the brass tube at 40°C is L_actual = 5 m × (1 + α_steel × 40) = 5 × 1.00044 = 5.0022 m. The brass tube's length at 0°C is L_0 = L_actual / (1 + α_brass × 40) = 5.0022 / 1.00076 ≈ 4.9984 m. This rounds to 4.999 m among the given options.

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Step-by-step solution

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