Question

Find the dimensions of `(axxb)/(c )` In the relation y= 4 sin at + 3 cos bt -ct, where t is time and y is distance.

Answer 1

The given relation is
`y = 4 sin at +3 cos bt -ct`
Here, `at = theta, a = (theta)/(t) = (1)/(T) = [T^(-1)]`
`bt = theta, b = (theta)/(t) =(1)/(T) = [T^(-1)]`
`c xx t = y, c = (y)/(t) = (L)/(T) = [ LT^(-1)]`
Now, `(axxb)/(c ) = [T^(-1)[T^(-1)])/([LT^(-1)] = [L^(-1) T^(-1)]`