An equilarteral triangle ABC is formed by joining three rods of equal length and Dis the mid point of AB. The coefficient of linear expansion for AB is alpha_(1) and for AC and BC is alpha_(2), if distance DC remains constant for small changes in temper- ature. Find the relation between alpha_(1) and alpha_(2)(##AKS_NEO_CAO_PHY_XI_V01_PMH_C12_SLV_016_Q01.png" width="80%">

An equilarteral triangle ABC is formed by joining three rods of equal

1.	An equilarteral triangle ABC is formed by joining three rods of equal length and Dis the mid point of AB. The coefficient of linear expansion for AB is alpha_(1) and for AC and BC is alpha_(2), if distance DC remains constant for small changes in temper- ature. Find the relation between alpha_(1) and alpha_(2)(##AKS_NEO_CAO_PHY_XI_V01_PMH_C12_SLV_016_Q01.png" width="80%">
Answer» SOLUTION :D is MID point condition to have CD constant `AC^(2) - AD^(2) `constant `L_(2)^(2) - (L_(1)^(2))/(4)` = constant Differentiating w.r.tt `2L_(2)(dL_(2))/(dt ) - 2 (L_(1))/(4) (dL_(1))/(dt) = 0 ` or `2L_(2) dL_(2) - 2 (L_(1))/(4) dL_(1) = 0` `dL_(2) = L_(2) alpha_(2) Delta theta and dL_(1) = L_(1) alpha Delta theta` ` 2 L_(2) , L_(2) alpha_(2) Delta theta = (L_(1))/(2) L_(1) theta_(1) Delta theta` but `L_(2) = L_(1)` `therefore 2 alpha_(1) = (1)/(2) alpha_(1) "or " 4 alpha_(2) = alpha_(1)`