Question

if y=a sin(bt+cX) where X and Y are displacement and t is time, then dimensional formula of a/BC is​

Answer 1

Given info : if y=a sin(bt+cx) where x and y are displacement and t is time.

To find : the dimensional formula of a/bc is ...

solution : here the equation is y = a sin(bt +cx)

we know, trigonometric identities are dimensionless quantities.

so, dimension of y = dimension of a

⇒ [L] = dimension of a

now have a look the part of (bt + cx), it is the angle of sine and we know that angle doesn't have dimension.

so, bt + cx = dimensionless

it means, bt and cx both are dimensionless quantities.

∵ bt = dimensionless

⇒ dimension of b = dimension of 1/t = [T⁻¹]

similarly, cx = dimensionless

⇒ dimension of c = dimension of 1/x = [L⁻¹]

now, the dimensional formula of a/bc = $\frac{[L]}{[T^{-1}][L^{-1}]}$ = [L²T]

therefore the dimensional formula of a/bc is [L²T]