Question

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.

• A. $x=1,y=1,z=-1$
• B. $x=1,y=-1,z=1$
• C. $x=-1,y=1,z=1$
• D. $x=1,y=1,z=1$

Answer 1

Answer: (B)

Substituting the dimension of given quantities in the relation provided by the problem ${\left[M{L}^{-1}{T}^{-2}\right]}^x{\left[M{T}^{-2}\right]}^y{\left[L{T}^{-1}\right]}^z={\left[MLT\right]}^0$ 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
$x=1;y=-1;z=1$