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question:an iron scale is calibarated at o degree celcius .The length of a zinc rod is measured to be 100cm by the scale when the rod and the scale both are at 0 degree celcius.what will be the length of the rod is measured by the scale when both are at 100 degree celcius.Give alfa iron =1.2*10^-5 +degree celcius and alfa zinc=2.6*10^-5/degree celcius

question:an iron scale is calibarated at o degree celcius .The length of a zinc rod is measured to be 100cm by the scale when the rod and the scale both are at 0 degree celcius.what will be the length of the rod is measured  by the scale when both are at 100 degree celcius.Give alfa iron =1.2*10^-5 +degree celcius and alfa zinc=2.6*10^-5/degree celcius 

Grade:12th pass

1 Answers

Rituraj Tiwari
askIITians Faculty 1792 Points
3 years ago
=> In the beginning, the rod and the scale both are at 0°C. Iron scale and rod both will expand at 100° C.

Suppose the length of zinc rod at 0 °C, Lz0 = 100 cm

αiron = 1.2 * 10⁻⁵ C⁻¹

αzink = 2.6 * 10⁻⁵ C⁻¹

=> The length of the rod as measured by the scale when both are at 100°C as it undergoes thermal expansion itself, L z t :

= L z 0 { 1 + ( αzinc − α Iron ) t }

= 100 {1 + ( 2.6 × 10 ⁻⁵ − 1.2 × 10 ⁻⁵) 100 }

= 100 {1 + ( 1.4 × 10 ⁻⁵ )10² }

= 100 { 1 + 1.4 * 10⁻³ }

= 100 {1 + 1.4/1000 }

= 100 { 1 + 0.0014}

= 100 { 1.0014 }

= 100.14 c m

Thus, the length of the rod as measured by the scale when both are at 100°C will be 100.14 cm.

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