Question

The diameters of steel rods A and B having the same length have 2cm and 4 cm respectively they are heated through 100 degree Celsius ℅.what is the ratio of increase of length of A to that ofB

Answer 1

The diameters of steel rods A and B having the same length have 2 cm and 4cm respectively they are heated through 100°C.

We have to find the ratio of increase of length of A and to that of B.

Increase in length due to increase in the temperature of it is given by, l = l₀(1 + α∆T)

• where l₀ is initial temperature.
• α is coefficient of linear expansion of steel rod.
• ∆T is the change in temperature of rod.

here you see, expansion of length only depends on , initial length, the coefficient of linear expansion and change in temperature. it doesn't depend on the diameter.

• but both the rods have equal length.
• both are steel rods so coefficient of linear expansion are same.
• and also changes in temperature are same.
• hence, the ratio of change in length must be 1 : 1.

Therefore the ratio of increase of length of A to that of B is 1 : 1.