Question

If Y = asin(bt + cx), where X and Yare displacement and tis time, then dimensional formula of a is bc​

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 ...(1)  

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] ...(2)  

similarly, cx = dimensionless

⇒ dimension of c = dimension of 1/x = [L⁻¹] ...(3)  

now, the dimensional formula of a/bc =  = [L²T]

[ from equations (1) , (2) and (3) ]  

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

Answer 2

Answer:

L^2T^1

Explanation:

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