Question

Qn.) If the following equation is dimensionally correct then obtain the
dimensions of X, Y & Z.
v= Xt? + Yt + Z ( where v = velocity & t= time )​

Answer 1

Explanation:

dimension of velocity = [L]/[T]

dimension of time = [T]

in equation:

Xt + Yt + Z

we can write

t(X+Y) + Z

Now we write Dimensions:

[T] ( X + Y ) + Z = [L]/[T]

[T]^2 (X+Y) + Z[T] = [L]

We can add x and y that means they have same dimension. This means:

X and Y dimension must be is [L] / [T]^2

Z dimension must be [L]/[T]