00:01
Hello students in this question we are given that a composite rod is made by joining two rods of different material but the same cross -sectional area as shown so let's see the figure so this type of composite rod is made and we have to design this rod using steel whose coefficient of linear expansion is given that is 11 multiplied by 10 to the power minus 6 per degree centigrade this is of steel and of brass is given to us which is 19 multiply by 10 to the 0 .6 per degree celsius and the total length is given to us that is 52 .4 centimeters and effective coefficient of linear expansion should be so l here alpha effective should be we write alpha effective should be equal to 13 multiply by 10 to the per minus 6 per degree celsius.
01:02
So we have to compute the length of steel and brass rod that must be used.
01:10
So let us see.
01:11
So this rod here we have.
01:13
So this is for this is alpha 1 and this is alpha 2 suppose this is of l1 length and this is of l2 length.
01:22
So we can write here l is equal to here l is equal to l1 plus l2.
01:30
Now we can write l is equal to 1 is equal to 1 plus l2.
01:31
Now we can write l1 is equal to 1 l multiply by 1 plus alpha delta t that is a change in length is equal to l1 1 plus alpha delta t plus l2 times 1 plus alpha delta t so when we solve this so here we get l alpha alpha delta t is equal to l 1 alpha alpha delta t plus l2 alpha alpha so here we have l alpha is equal to l1 alpha 1 plus l2 alpha 2.
02:11
Now we know that we can write from here that here l2 is equal to l minus l1.
02:20
This we can write from the expression.
02:23
So in this expression we can write l alpha is equal to l1 alpha 1 plus l alpha 2 because in place of l2 we write l minus l2.
02:35
Minus l1 alpha 2...