Question

Two rods of different materials having coefficients of thermal expansion  and Young’s modulii Y1Y2 respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If  the thermal stresses developed in the two rods are equal provided Y1 : Y2 is equal to:

Solution

Correct option is

3 : 2

 

Let l be the original length of the rods. Let them be heated so that the increase in temperature is toC.

Increase in length = 

Where  is the coefficient of linear expansion of the rod

                    Strain = 

                     Stress = 

Stresses are equal for the two rods if

                   

or                     

SIMILAR QUESTIONS

Q1

A drilling machine of power P watts is used to drill a hole in copper block of mass M kg. If the specific heat of a copper is s J  and 40% of  the power is lost due to heating of the machine, the rise in the temperature of the block in T seconds will be (in oC)

Q2

A geyser, operating on LPG (liquefied petroleum gas) heats water flowing at the rate of 3.0 litres per minute, from 27oC to 77oC. If the heat of combustion of LPG is , how much fuel in grams is consumed per minute?

Q3

A copper block of mass 2 kg is heated to a temperature of 500oC and then placed in a large block of ice at 0oC. What is the maximum amount of ice that can melt? The specific heat of copper is 400 j  and latent heat of fusion of water is .

Q4

The dimensions of the coefficient of thermal conductivity are

Q5

Two different metal rods of the same length have their ends kept at the same temperatures and  with . If A and are their cross-sectional areas and k1 and k2 their thermal conductivities, the rate of flow of heat in the two rods will be the same if

Q6

Two rods A and B of different materials are welded together as shown in Fig. If their thermal conductivities are k1 and k2 , the thermal conductivity of the composite rod will be

                                                        

Q7

A one liter flask contains some mercury. It is found that at different temperatures the volume of air inside the flask remains the same. What is the volume of mercury in the flask? Given the coefficient of linear expansion of glass  oC–1, the coefficient of volume expansion of mercury is  oC–1.

Q8

A wire of cross-sectional area A at temperature t is held taut with negligible tension between two rigid supports. If the wire is cooled to a temperature  what tension is developed in the wire? The coefficient of linear expansion is  and the Young’s modulus of the wire is Y.

Q9

Two uniform brass rods A and of length l and 2and radii 2r and rrespectively are heated to the same temperature. The ratio of the increase in the length of A to that of B is

Q10

The water equivalent of a copper calorimeter is 4.5 g. If the specific heat of copper is 0.09 cal.g–1oC–1 the