Three rods of equal of length are joined...

Three rods of equal of length are joined to from an equilateral triangle ABC. `D` is the midpoint of AB. The coefficient of linear expansion is `alpha_(1)` for AB and `alpha_(2)` for `AC` and `BC` . If the distance `DC` remains constant for small changes in temperature,

`alpha_1 = alpha_2`

`alpha_1 =2 alpha_2`

`alpha_1 = 4 alpha_2`

`alpha_1 = 1/2 alpha_2`

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The correct Answer is:

`DC^2 =AC^2 -AD^2 =l^2 - ((1)/(2))^2`
` DC^2 = [l (1+ alpha_2 t) ]^2 = [(1)/(2) (1+ alpha_t t)]^2`
`l^2 - (l^4)/(4) = l^2 =(1+ alpha _(2)^(2) t^2 + 2alpha _(2) t ) -(l^2)/(4) (1+ alpha_(1)^(2) t^2 + 2 alpha_1 t)`
Neelecting ` alpha_(2)^(2) t^2` and ` alpha_(1)^(2) t^2 , 0 = l^2 ( 2 alpha_1 t ) - (l^2)/(4) ( 2 alpha _1 t)`
` 2 alpha _2 = ( 2 alpha_1)/( 4) implies alpha_2`

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An equilateral triangle ABC is formed by joining three rods of equal length and D is the mid-point of AB . The coefficient of linear expansion for AB is alpha_(1) and for AC and BC is alpha_(2) . The relation between alpha_(1) and alpha_(2) , if distance DC remains constant for small changes in temperture is

`alpha_(1) = alpha_(2)`

`alpha_(1) = 4alpha_(2)`

`alpha_(2) = 4alpha_(1)`

`alpha_(1) = (1)/(2)alpha_(2)`

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,

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

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

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

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

Three rods of equal l are joined to from an equilateral trangle PQR.O is the mid-point of PQ. Distance OR remains same for small change in temperature. Coefficient of linear expansion for PR and RQ is same i.e., alpha_(2) but for PQ is alpha_(1^.) Then

`alpha_(2) = 3 alpha_(1)`

`alpha_(2) = 4 alpha_(1)`

`alpha_(1) = 3 alpha_(2)`

`alpha_(1) = 4 alpha_(2)`

Three rods of equal of length are joined to from an equilateral triangle ABC. `D` is the midpoint of AB. The coefficient of linear expansion is `alpha_(1)` for AB and `alpha_(2)` for `AC` and `BC` . If the distance `DC` remains constant for small changes in temperature,

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Three rods of equal l are joined to from an equilateral trangle PQR.O is the mid-point of PQ. Distance OR remains same for small change in temperature. Coefficient of linear expansion for PR and RQ is same i.e., alpha_(2) but for PQ is alpha_(1^.) Then

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