00:01
In this question, we have to form a dimensionless ratio.
00:04
Now, here we can say that the dimensions of g will be equals to, let us write, this will be here l and then here it is t raised to the power negative 2 and if we talk about the dimensions of d, then it will be here l.
00:21
Now, if we talk about the dimensions of rho then it will be here let us write it is ml raised to the power negative 3 now the dimensions of p can be here written to be equals to let us write this is ml and then it will be negative 1 and then here it is t raised to the power negative 2 so from this information we can say by using the buckingham method buckingham pi method actually so here the product will be equals to let us write this is going to be here p raised to the power a and then it will be here g raised to the power b now here it is d raised to the power c and rho will be there as such and this is because we are having four variables and three fundamental variables.
01:13
So we have formed this very dimensionless ratio and here this pi denotes a dimensionless number so, its dimensions are m raised to the power 0 and then l raised to the power 0, t raised to the power 0.
01:27
So, if we plug in the value in the right hand side of this very expression then we will be here having let us write this is going to be m, l raised to the power negative 1, t raised to the power negative 2 and then here it is raised to the power a.
01:43
Now, it will be here g raised to the power b which is going to be l, t raised to the the power negative 2 and then here it is b.
01:52
Now the value of here d that is the dimensions of d will be l raised to the power c and the dimensions of rho will be ml raised to the power negative 3...