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The coefficient of linear expansion of a...

The coefficient of linear expansion of an in homogeneous rod change linearly from `alpha_(1)` to `alpha_(2)` from one end to the other end of the rod. The effective coefficient of linear expansion of rod is

A

` alpha_(1) + alpha_(2)`

B

`( alpha_(1)+ alpha_(2))/(2)`

C

`sqrt( alpha_(1)alpha_(2))`

D

`alpha_(1)-alpha_(2)`

Text Solution

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The correct Answer is:
B
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Knowledge Check

  • Two rods of lengths L_(1) and L_(2) are welded together to make a composite rod of length (L_(1)+L_(2)) . If the coefficient of linear expansion of the materials of the rod are alpha_(1) and alpha_(2) respectively. The effective coefficient of linear expansion of the composite rod is

    A
    `(L_(1)alpha_(1) - L_(2)alpha_(2))/(L_(1) + L_(2))`
    B
    `(L_(1)alpha_(1) + L_(2)alpha_(2))/(L_(1) + L_(2))`
    C
    `sqrt(alpha_(1)alpha_(2))`
    D
    `(alpha_(1) + alpha_(2))/(2)`

  • In an isotropic medium, the coefficients of linear expansion of a solid are alpha_(1), alpha_(2) and alpha_(3) in three mutually perpendicular directions. The coefficient of volume expansion for the solid is

    A
    `alpha_(1)-alpha_(2) + alpha_(3)`
    B
    `(alpha_(1) + alpha_(2) + alpha_(3))/(3)`
    C
    `alpha_(1)+ alpha_(2) + alpha_(3)`
    D
    None of these

  • The coefficient of linear expansion varies linearly from alpha_(1) to alpha_(2) in a rod of length l. Find the increase in length when the temperature is increased by DeltaT .

    A
    `((alpha_(1)+alpha_(2))/(2))lDeltaT`
    B
    `(alpha_(1)+alpha_(2))lDeltaT`
    C
    `(alpha_(1)+(alpha_(2))/(2))lDeltaT`
    D
    `((alpha_(1))/(2)+alpha_(2))lDeltaT`

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