Q. 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) $a = 1,b = 1,c = 1$
Explanation
Here, $\left\lbrack M^{0}L^{0}T^{0} \right\rbrack = \left\lbrack M^{\ }L^{- 1}T^{- 2} \right\rbrack^{a}\left\lbrack MT^{- 3} \right\rbrack^{b}\left\lbrack LT^{- 1} \right\rbrack^{c}$ Or $\left\lbrack M^{0}L^{0}T^{0} \right\rbrack = {\lbrack M}^{a + b}L^{- a + c}T^{- 2a - 3b - c}$] Comparing powers of $M,L$ and $T,$ we get $a + b = 0, - a + c = 0, - 2a - 3b = 0$ Solving $a = 1,b = - 1,c = 1$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.