Home
Class 11
PHYSICS
An iron wire AB of length 3 m at 0^(@)C ...

An iron wire AB of length `3 m` at `0^(@)C` is stretched between the oppsote walls of a brass casing at `0^(@)C`. The diameter of the wire is `0.6mm`. What extra tension will be set up in the wire when the temperature of the system is rasied to `40^(@)C`?
Given `a_("brass")=18xx10^(-6)//k`
`a_("iron")=12xx10^(-6)//K`
`Y_("iron=21xx10^(10)N//m^(2)`

Text Solution

Verified by Experts


Increase in length of the iron wire
`=Ia Deltat=Ixx12xx10^(-6)xx40`
`=48Ixx10^(-5)m`
Increase in length of the brass tube
`=Ia Deltat=Ixx18xx10^(-6)xx40`
`=72Ixx10^(-5)m`
Since the increase in length of the brass tube is greater than that of the iron wire, the latter will be tightend. Let T be the tension in the wire. Then
Stress `=(T)/(pir^(2))=(T)/(pi(3xx10^(-4))^(2))=(T)/(9pixx10^(-8))`
Strain `=((721-48I)xx10^(-5))/(I)=24xx10^(-5)`
Since stress `=Yxx"Strain", (T)/(9pixx10^(-8))=21xx10^(10)xx24xx10^(-5)`
`7=21xx10^(10)xx9pixx10^(-8)=14.2N`
Promotional Banner

Topper's Solved these Questions

  • CALORIMETRY

    CENGAGE PHYSICS|Exercise Integer|8 Videos

  • BASIC MATHEMATICS

    CENGAGE PHYSICS|Exercise Exercise 2.6|20 Videos

  • CENTRE OF MASS

    CENGAGE PHYSICS|Exercise INTEGER_TYPE|1 Videos

Similar Questions

Explore conceptually related problems

An iron wire AB has diameter of 0.6 mm and length 3 m at 0^(@)C . The wire is now stretched between the opposite walls of a brass casing at 0^(@)C . What is the extra tension that will be set up in the wire when the temperature of the system is raised to 40^(@)C ? Givne alpha_("brass")=18xx10^(-6)//K alpha_("iron")=12xx10^(-6)//K Y_("iron")=21xx10^(10)N//m_^(2)

A heavy brass bar has projections at its ends as shown in the figure. Two find steel wires, fastened between the projections, are just taut (zero tension) when the whole systeam is at 0^(0)C . What is the tensile stress in the steel wires when the temperature of the systeam is raised to 300^(0)C ? Given that alpha_("brass") = 20 xx 10^(-6 ^(@))C^(-1) alpha_("steel") = 12 xx 10^(-6@)C^(-1) Y_("steel") = 2 xx 10^(11) Nm^(-2)

A fine steel wire of length 4 m is fixed rigidly in a heavy brass frame as ashown in figure . It is just taut at 20^(@)C . The tensile stress developed in steel wire it whole system is heated to 120^(@)C is :- ( Given alpha _("brass") = 1.8 xx 10^(-5) .^(@)C^(-1), alpha_("steel") = 1.2 xx 10^(-5) .^(@)C, Y_("steel") = 2 xx 10^(11) Nm^(-2), Y_("brass")= 1.7xx10^(7) Nm^(-2) )

A brass rod and a lead rod each 80 cm long at 0^@C are clamped together at one end with their free ends coinciding. The separatioin of free ends of the rods if the system is placed in a steam bath is ( alpha_("brass")=18xx10^(-6)//^(@)C and alpha_("lead")=28xx10^(-6)//^(@)C )

A wire of cross sectional area 3 mm^(2) is just stretched between two fixed points at a temperature of 20^(@)C . Then the tension in the wire when the temperature falls to 10^(@)C is, (alpha =1.2 xx 10^(-5) //""^(@)C, Y=2xx10^(11) N//m^(2))

A steel wire 2mm in diameteris ust streched between two dixed point at a temperature of 20^(@)C . Determine its tension when its temperature falls to 10^(@)C . Linear expansivity of steel =11 xx 10^(-6)//K, Young modulus =2 xx 10^(11)//m^(-2)

The diameter of an iron wire is 1.20 mm. If the speed of transverse waves in the wire is 50.0m//s , what is the tension in the wire? The density of iron is 7.7xx10^(3)kg//m^(3)

A steel wire 2mm in diameter is stretched between two clamps, when its temperature is 40^@C Calculate the tension in the wire, when its temperature falls to 30^@C Given, coefficient Y for steel = 21 xx 10^(11) dyn e//cm^2