Question

If $p$ represents radiation pressure, $c$ represents speed of light and $q$ represents radiation energy striking a unit area per second, then non-zero integers $a,b$ and $c$ are such that $p^a{q}^b{c}^c$ is dimensionless, then

• A. a = 1, b = 1, c = -1
• B. a = 1, b = -1, c = 1
• C. a = -1, b = 1, c = 1
• D. a = 1, b = 1, c = 1

Answer 1

Answer: (B)

Here, $\left[M^0{L}^0{T}^0\right]={\left[M{L}^{-1}{T}^{-2}\right]}^a{\left[M{L}^{-3}\right]}^b{\left[L{T}^{-1}\right]}^c$
Or $\left[M^0{L}^0{T}^0\right]=\left[M^{a+b}{L}^{-a+c}{T}^{-2a-3b-c}\right]$
Comparing powers of $M,L$ and $T$, we get
$a+b=0,-a+c=0,-2a-3b=0$
Solving, $a=1,b=-1,c=1$