Question

Consider the equation
v = 1/4zxt^2.
The dimensions of the variables v, x, and t are [L]/[T], [L], and [T], respectively. The numerical factor 4 is dimensionless. What must be the dimensions of the variable z, such that both sides of the equation have the same dimensions?

Answer 1

L * T^-1 = ? L T^2
? = T^-3
OR DO YOU MEAN???? v = 1/(4zxt^2) ????
L * T^-1 = x^-1 L^-1 T^-2
x^-1 = L^2 T^1
so
L^-2 T^-1
or
1/(L^2T)

Answer 2

1/[T]3

Answer 3

T^-3