## Question

Two rods of different materials having coefficient of thermal expansion and Young’s modulii *Y*_{1} and *Y*_{2} are fixed between two rigid and massive walls. The rods are heated to the same temperature. If there is no bending of the rods, the thermal stresses developed in them are equal provided

### Solution

If a rod of length *L *and coefficient of thermal expansion is heated to a temperature *t*, the increase in the length is given by

And

Since the value of *t *is the same for the two rods, the stresses in them will be equal if

or

#### SIMILAR QUESTIONS

A linear accelerator consists of a hundred brass discs tightly fitted into a steel tube. At 40^{o}C the diameter of each disc is 10.02 cm. The system is assembled by cooling the discs in dry ice at – 60^{o}C to enable them to slide into the close fitting tube. If the coefficient of expansion of brass is per ^{o}C, the diameter of each disc in dry ice will be

When a solid metallic sphere is heated, the largest percentage increase occurs in its

A steel scale measures the length of a copper rod as *L* cm when both are at 20^{o}C, the calibration temperature for the scale. If the coefficient of linear expansion for steel and copper are respectively, what would be the scale reading (in cm) when both are at 21^{o}C?

At 40^{o}C, a brass rod has a length 50 cm and a diameter 3.0 mm. It is joined to a steel rod of the same length and diameter at the same temperature. What is the change in the length of the composite rod when it is heated to 240^{o}C? The coefficient of linear expansion of brass and steel are respectively.

A metallic container is completely filled with a liquid. The coefficient of linear expansion of the metal is per ^{o}C and the coefficient of cubical expansion of the liquid is per ^{o}C. On heating the vessel,

A thin metal square plate has length *l*. When it is heated from 0^{o}C to 100^{o}C, its length increases by 1%. What is the percentage increase in the area of the plate?

A glass flask of volume 500 cm^{3} is completely filled with a liquid at 0^{o}C. When it is placed in boiling water at 100^{o}C, 75 cm^{3} of the liquid overflows. If the coefficient of cubical expansion of glass is ^{o}C^{-1}, what is the coefficient of cubical expansion of the liquid?

A thin metal square plate has length *l*. When it is heated from 0^{o}C to 100^{o}C, its length increases by 1%. What is the percentage increase in the area of the plate?

The density of a liquid of coefficient of cubical expansion . When the liquid is heated to a temperature *T*, the change in density will be

300 g of water at 25^{o}C is added to 100 g of ice at 0^{o}C. The final temperature of the mixture is