Question

If $p$ represents radiation pressure, $C$ represents the 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, $\left[M^{0} L^{0} T^{0}\right]=\left[M^{ \, } L^{- 1} T^{- 2}\right]^{a}\left[M T^{- 3}\right]^{b}\left[L T^{- 1}\right]^{c}$
Or $\left[M^{0} L^{0} T^{0}\right]=\left[\right. M^{a + b}L^{- a + c}T^{- 2 a - 3 b - c}$ ]
Comparing powers of $M,L$ and $T,$ we get
$a+b=0,-a+c=0,-2a-3b=0$
Solving $a=1,b=-1,c=1$