**Solution:**

The given relation F = mv^{2}, where **F** is the force,** m** is the mass and **v** is the speed of the particle.

The dimension of force **F = [MLT ^{-2}]**

The dimension of velocity, **v = [LT ^{-1}]**

The dimension of mass **m = [M]**

The dimension of left hand side,** F = [MLT ^{-2}]**

Dimension of the right hand side** mv ^{2} = [M][LT^{-1}]^{2} = [ML^{2}T^{-2}]**

Since the dimensions on the left-hand side are not equal to the dimension on the right-hand side of the equation. So, the formula is dimensionally wrong.