The dimensions of physical quantity X in the equation Force = X / Density is given by

The correct option is M² L⁻² T⁻².

To find the dimensions of the physical quantity $X$ in the given equation, we start with the formula:
$\text{Force}=\frac{X}{\text{Density}}$
Rearranging the equation to solve for $X$, we get:
$X=\text{Force}\times \text{Density}$

Now, let us determine the dimensional formula for each quantity involved:

1. Force is defined as mass times acceleration ($F=ma$).
The dimensions of mass are [M].
The dimensions of acceleration (velocity/time) are [L T^-2].
Therefore, the dimensional formula of Force is:
$\left[\text{Force}\right]=\left[{\text{M L T}}^{-2}\right]$

2. Density is defined as mass per unit volume ($\rho =\frac{m}{V}$).
The dimensions of mass are [M].
The dimensions of volume are [L³].
Therefore, the dimensional formula of Density is:
$\left[\text{Density}\right]=\left[{\text{M L}}^{-3}\right]$

Now, we substitute these dimensions back into the rearranged equation for $X$:
$\left[X\right]=\left[\text{Force}\right]\times \left[\text{Density}\right]$
$\left[X\right]=\left[{\text{M L T}}^{-2}\right]\times \left[{\text{M L}}^{-3}\right]$
Combining the exponents of the fundamental quantities (M, L, and T):
$\left[X\right]=\left[{\text{M}}^{1+1}{\text{L}}^{1-3}{\text{T}}^{-2}\right]$
$\left[X\right]=\left[{\text{M}}^2{\text{L}}^{-2}{\text{T}}^{-2}\right]$

Thus, the dimensions of the physical quantity $X$ are given by M² L⁻² T⁻².