It is given that  P, C and Q represent radiation pressure, speed of light and radiation energy striking a unit area per second respectively. Determine the values of non-zero integers x, y and z such that the quantity $P^x{Q}^y{C}^z$ is dimensionless.

Substituting the dimension of given quantities in the relation provided by the problem

${\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right]}^{\mathrm{x}}{\left[{\mathrm{MT}}^{-2}\right]}^y{\left[{\mathrm{LT}}^{-1}\right]}^{\mathrm{z}}$

$=[\mathrm{MLT}{]}^0$

Comparing the power of M, L, T in both L.H.S and R.H.S,

we get

$x+y=0\dots \text{...(i) }$

$-x+z=0\dots \left(ii\right)$

$-2x-2y-z=0\dots \left(\mathrm{iii}\right)$

After solving the above equations

we get

$x=1;y=-1;z=1$