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