Question

A meter rod made of steel is correct at 0°C
and other meter rod of same material is correct
at 30°C. If a = 12 x 10-6/°C, the difference
between their lengths at 20°C is

Answer 1

Therefore the difference between lengths at 20°C is 0.036 cm.

Given : A meter rod made of steel is correct at 0°C and other meter rod of same material is correct at 30°C. If a = 12 x 10¯6/°C.

To find : The difference between their lengths at 20°C

solution : A meter rod made of steel is correct at 0°C. i.e., l = 1 m

so length of rod at 20°C , l₁ = l(1 + α∆T)

= 1 × {1 + 12 × 10^-6 × (20 - 0)}

= 1 + 12 × 10^-6 × 20

= 1 + 0.000240

= 1.00024 m

again, The other meter rod of same material is correct at 30°C i.e., l = 1 m

so length of rod at 20°C , l₂= 1 × {1 + 12 × 10^-6 × (20°C - 30°C)}

= 1 - 12 × 10^-6 × 10

= 1 - 0.000120

⇒0.99988 m

so the difference between lengths at 20°C = l₁ - l₂

= 1.00024 - 0.99988

= 0.00036 m

= 0.036 cm

Therefore the difference between lengths at 20°C is 0.036 cm