Magnitude of force F experienced by a certain object moving with speed v is given by F = Kv²,where K is a constant. Find the dimensions of K.

The correct option is [ML⁻¹].

To find the dimensions of the constant $K$, we start with the given formula:
$F=K{v}^2$
Rearranging the equation to solve for $K$ gives:
$K=\frac{F}{v^2}$

Next, we determine the dimensional formulas for each of the quantities involved:
1. Force ($F$) is defined as mass times acceleration ($F=ma$). Its dimensional formula is:
$\left[F\right]=\left[ML{T}^{-2}\right]$
2. Velocity or speed ($v$) is distance over time. Its dimensional formula is:
$\left[v\right]=\left[L{T}^{-1}\right]$
Therefore, the square of the speed ($v^2$) has the dimensions:
$\left[v^2\right]={\left[L{T}^{-1}\right]}^2$

Now, substitute the dimensions of $F$ and $v^2$ back into the rearranged equation to find the dimensions of $K$:
$\left[K\right]=\frac{\left[ML{T}^{-2}\right]}{\left[L^2{T}^{-2}\right]}$
Simplifying the expression by subtracting the exponents of like bases:
$\left[K\right]=\left[M{L}^{1-2}{T}^{-2-(-2)}\right]$
$\left[K\right]=\left[M{L}^{-1}{T}^0\right]=\left[M{L}^{-1}\right]$

Thus, the dimensional formula of the constant $K$ is [ML⁻¹].