Question

three rods of same length are arranged to form an equilateral triangle. two rods made of the same material of coefficient of linear expansion alpha1 , and the third rod which forms the base of the triangle has coefficient of expansion alpha2. the altitude of the triangle will remain the same at all temperatures if alpha1/alpha2​

Answer 1

Answer:

Solution

 DC2=AC2−AD2                                  

                =ℓ2−(2ℓ)2

                =[ℓ(1+∝2t)]2−[2ℓ(1+∝1t)]2

                ℓ2−4ℓ2=ℓ2(1+∝22t2+2∝2t)−4ℓ2(1+∝12t2+2∝2t)

                0=ℓ2(2∝2t)−4ℓ2(2∝1t)

                2∝2=

Explanation:

The coefficient of linear expansion of a rod of length 1 m, at 27o C is, varying with temperature as α=2/T unit(300K≤T≤600K) where T is the temperature of rod in Kelvin. The increment in the length of rod if its temperature increases from 27oC to 327oC is 

Medium

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A rectangular plate is made of a material of coefficient of linear expansion of ′α′ , its size is (a×b). two circular hole of radii R1andR2 has been cut with a separation between their centres as 'x'at a higher temperature 't'if the final perameters are a1,b1,R11,R21 and 'x'are the respective values at higher temperature 't' then (aa1)×(bb1)×(R

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