Q. 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.
NTA AbhyasNTA Abhyas 2020
Solution:
Substituting the dimension of given quantities in the relation provided by the problem $\left[ML^{- 1} T^{- 2}\right]^{x}\left[MT^{- 2}\right]^{y}\left[LT^{- 1}\right]^{z}=\left[MLT\right]^{0}$ Comparing the power of $M,L, \, T$ in both L.H.S and R.H.S, we get
$x+y=0$ ...(i)
$-x+z=0$ ...(ii)
$-2x-2y-z=0$ ...(iii)
After solving the above eqyations we get
$x=1;y=-1;z=1$
$x+y=0$ ...(i)
$-x+z=0$ ...(ii)
$-2x-2y-z=0$ ...(iii)
After solving the above eqyations we get
$x=1;y=-1;z=1$