Question

Two rods of different materials having coefficient of thermal expansion  and Young’s modulii Y1 and Y2 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

Correct option is

 

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

                                    

 

And                  

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

                    

or                          

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

A steel scale measures the length of a copper rod as L cm when both are at 20oC, 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 21oC?

Q4

At 40oC, 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 240oC? The coefficient of linear expansion of brass and steel are respectively.

Q5

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

Q6

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

Q7

A glass flask of volume 500 cm3 is completely filled with a liquid at 0oC. When it is placed in boiling water at 100oC, 75 cm3 of the liquid overflows. If the coefficient of cubical expansion of glass is  oC-1, what is the coefficient of cubical expansion of the liquid?

Q8

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

Q9

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

Q10

300 g of water at 25oC is added to 100 g of ice at 0oC. The final temperature of the mixture is