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Two rods, one of aluminium and other mad...

Two rods, one of aluminium and other made of steel, having initial lengths `l_(1) and l_(2)` are connected together to form a single rod of length `(l_(1)+l_(2))`. The coefficient of linear expansions for aluminium and steel are `alpha_(a)` and `alpha_(s)` respectively. If length of each rod increases by same amount when their tempertures are raised by `t^(@)C`, then find the ratio `l_(1) (l_(1)+l_(2))`.

A

`(alpha_(s))/(alpha_(a)+alpha_(s))`

B

`(alpha_(s))/(alpha_(a)-alpha_(s))`

C

`(alpha_(a) + alpha_(s))/(alpha_(s))`

D

None of these

Text Solution

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The correct Answer is:
A
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Two rods, one of aluminium and other made of steel, having initial lenghts l_(1) and l_(2) are connected together to form a singel rod of length (l_(1)+l_(2)) . The coefficient of linear expansions for aluminium and steel are alpha_(a) and alpha_(s) respectively. If length of each rod increases by same amount when their tempertures are raised by t^(@)C , then find the ratio l_(1) (l_(1)+l_(2)) .

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

Knowledge Check

  • Two rods, one of aluminium and the other made of steel, having initial length l_1 and l_2 are connected together to from a single rod of length l_1+l_2. The coefficients of linear expansion for aluminium and steel are alpha_a and alpha_s and respectively. If the length of each rod increases by the same amount when their temperature are raised by t^0C, then find the ratio l_1//(l_1+l_2)

    A
    `(alpha_s)//(alpha_a)`
    B
    `(alpha_a)//(alpha_s)`
    C
    `(alpha_s)//((alpha_a)//(alpha_s))`
    D
    `(alpha_a)//((alpha_a)//(alpha_s))`

  • Two rods , one of aluminium and the other made of steel, having initial length l_(1) and l_(2) are connected together to from a sinlge rod of length l_(1)+l_(2) . The coefficient of linear expansion for aluminium and steel are alpha_(a) and alpha_(s) for AC and BC . If the distance DC remains constant for small changes in temperature,

    A
    `(alpha_(s))/(alpha_(a))`
    B
    `(alpha_(a))/(alpha_(s))`
    C
    `(alpha_(s))/((alpha_(a)+alpha_(s)))`
    D
    `(alpha_(a))/((alpha_(a)+alpha_(s)))`

  • 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)`

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