Question

y=A log (AB/C + t ) where y be displacement and t be time then find out the dimension of A, B, and C ?

Answer 1

The dimensions of A, B, and C are the same as the dimensions of displacement (y).

Step-by-step explanation:

The given equation is y = A log (AB/C + t), where y represents displacement and t represents time. We need to find the dimensions of A, B, and C.

The logarithmic function does not have any units or dimensions. Therefore, the dimensions of the argument of the logarithm on the right-hand side of the equation must be the same as the dimensions of the displacement, which is represented by y.

Using dimensional analysis:

1. The argument of the logarithm (AB/C + t) has the same dimensions as displacement (y).
2. Since AB/C is an addition operation, its dimensions must be the same as displacement (y).
3. Since A, B, and C do not have any algebraic operations with other variables, their dimensions will be the same as the dimensions of the displacement (y).

Therefore, the dimensions of A, B, and C are the same as the dimensions of displacement (y).