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 = [ML2T2]
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.