Home
Class 11
PHYSICS
A uniform metal rod fixed at its ends of...

A uniform metal rod fixed at its ends of `2 mm^(2)` cross-section is cooled from `40@^C` to `20^@C`. The coefficient of the linear expansion of the rod is `12xx10^(-6) ` per degree celsius and its young's modulus of elasticity is `10^11 N//m^(2).` The energy stored per unit volume of the rod is

A

`2880 J//m^(3)`

B

`1500 J//m^(3)`

C

`5760 J//m^(3)`

D

`1440 J//m^(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
`Deltal = lalpha Deltatheta= (Deltal)/(l) = (alpha Delta theta)`
` "Stress" = Yxx"Strain" = Yalpha Delta theta` ltbr. Energy stored per unit volume
`= 1/2xx "Stress"xx "Strain"`
`1/2xxYxx(alpha Delta theta)^(2)`
` = 1/2xx10^(11)xx(12xx10^(-6)xx20)^(2)`
`= 2880 J//m^(3)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • ELASTICITY

    DC PANDEY|Exercise Level 2 More Than One Correct|8 Videos

  • ELASTICITY

    DC PANDEY|Exercise Level 2 Comprehension Based|6 Videos

  • ELASTICITY

    DC PANDEY|Exercise Level 1 Subjective|8 Videos

  • CURRENT ELECTRICITY

    DC PANDEY|Exercise All Questions|434 Videos

  • ELECTROSTATICS

    DC PANDEY|Exercise Integer|17 Videos

Similar Questions

Explore conceptually related problems

A uniform copper rod of length 50 cm and diameter 3.0 mm is kept on a frictionless horizontal surface at 20^(@)C . The coefficient of linear expansion of copper is 2.0 xx 10^(-5) K^(-1) and Young's modulus is 1.2 xx 10^(11) N//m^(2) . The copper rod is heated to 100^(@)C , then the tension developed in the copper rod is

The area of cross-section of railway track is 0.01 m^(2) . The temperature variation is 10^(@)C . Coefficient of linear expansion of steel =10^(-5)//""^(@)C . (Young's modulus of steel = 10^(11) Nm^(-2) ). Calculate the energy stored per meter in the track.

Knowledge Check

  • A uniform metal rod of 2mm^(2) area of cross section is heated from 0^(@)C to 20^(@)C . The coefficient of linear expansion of the rod is 12xx10^(-6)//""^(@)C . Its Young's modulus of elasticity is 10^(11)N//m^(2) , then the energy stored per unit volume of rod is,

    A
    `1440 J//m^(3)`
    B
    `2880 J//m^(3)`
    C
    `1200 J//m^(3)`
    D
    `3880J//m^(3)`

  • The coefficient of linear expansion of a metal rod is 12 xx 10^(-6//0)C , its value in per ^(0)F

    A
    `(20)/(3) xx 10^(-6//0)F`
    B
    `(15)/(4) xx 10^(-6//0)F`
    C
    `21.6 xx 10^(-6//0)F`
    D
    `12 xx 10^(-6//0)F`

  • A uniform rod of cross-section 4 mm^(2) is heated from 0^(@)C " to "10^(@)C. The coefficient of linear expansion of the rod, prop=12xx10^(-6)//^(@)C and Young's modulus =10^(11)N//m^(2). The strain produced in the rod is

    A
    `8xx10^(-4)`
    B
    `12xx10^(-4)`
    C
    `8xx10^(-5)`
    D
    `12xx10^(-5)`

    • Similar Questions

    Explore conceptually related problems

    A metal rod undergoes an elastic strain of 0.04% and the Young's modulus of the material is 3.6xx10^(10)N//m^(2) . The energy per unit volume stored in the rod in Jule/ m^(3) is

    A metallic rod of Young's modulus 2xx10^(11)Nm^(2) undergoes a strain of 0.5% . Then the energy stored per unit volume in the rod will be

    A rod is fixed between two points at 20^(@)C . The coefficient of linear expansion of material of rod is 1.1 xx 10^(-5)//.^(C and Young's modulus is 1.2 xx 10^(11) N//m . Find the stress develop in the rod if temperature of rod becomes 10^(@)C

    The young's modulus of the material of a rod is 20xx10^(10) pascal. When the longitudal strain is 0.04% . The energy stored per unit volume is

    A uniform metal rod is used as a bar pendulum. If the room temperature rises by 10^(@)C , and the coefficient of linear expansion of the metal of the rod is 2 xx 10^(-6) per^(@)C , the period of the pendulum will have percentage increase of

    Home
    Profile