The dimensions of physical quantity $X$ in the equation $\text{Force} = \frac{X}{\text{Density}}$ are given by:

The position of a particle at time $t$ is given by the relation $x(t) = \left( \frac{v_0}{\alpha} \right) (1 - e^{-\alpha t})$,where $v_0$ is a constant and $\alpha > 0$. The dimensions of $v_0$ and $\alpha$ are respectively:

If $C$ is the velocity of light,$h$ is Planck's constant,and $G$ is the gravitational constant,and these are taken as fundamental quantities,then the dimensional formula of mass is:

The time dependence of a physical quantity $P$ is given by $P = P_0 \exp(-\alpha t^2)$,where $\alpha$ is a constant and $t$ is time. The constant $\alpha$:

From the following,the quantity (constructed from the basic constants of nature) that has the dimensions of length,as well as the correct order of magnitude for a typical atomic size,is:

The speed of light $(c)$,gravitational constant $(G)$,and Planck's constant $(h)$ are taken as fundamental units in a system. The dimensions of time in this new system should be