Q. If $P$ represents radiations pressure, $c$ represents speed of light and $Q$ represents radiation energy striking a unit area per $second$, the non-zero integers $x,\ y\$and $z$ such that $P^{x}Q^{y}c^{z}$ is dimensionless, are
A) $x = 1,\ y = 1,\ z = - 1$
B) $x = 1,\ y = - 1,\ z = 1$
C) $x = - 1,\ y = 1,\ z = 1$
D) $x = 1,\ y = 1,\ z = 1$
Explanation
By substituting the dimension of given quantities $\left\lbrack ML^{- 1}T^{- 2} \right\rbrack^{x}\left\lbrack MT^{- 3} \right\rbrack^{y}\left\lbrack LT^{- 1} \right\rbrack^{z} = \lbrack MLT\rbrack^{0}$ By comparing the power of $M,L,T$ in both sides $x + y = 0$ ...(i) $- x + z = 0\$ …(ii) $- 2x - 3y - z = 0\$ …(iii) The only values of $x,\ y,\ z$ satisfying (i), (ii) and (iii) corresponds to (b)
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.