**Solution:**

The given formula is, \(p=\sqrt{\frac{2mE}t}\)

Where,

**P** is the momentum,

**m** is the mass,

**E** is the energy, and

**t** is the time

The dimension of each terms are as follows:

dimension of momentum, p = [MLT^{-1}],

dimension of mass, m = [M],

dimension of time, t = [T], and

dimension of energy, E = [ML^{2}T^{2}]

Now, substituting the quantities in the above-given relation, we get,

\(\left[MLT^{-1}\right]=\sqrt{\frac{M.ML^2T^{-2}}T}\), *because 2 is dimensionless constant*

\(=\sqrt{M^2L^2T^{-1}}\)

\(=MLT^{-\frac12}\)

Dimension of LHS ≠ Dimension of RHS

**So, the formula is dimensionally incorrect.**