If P represents radiation pressure,c represen | vedclass

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Question

(B) The dimensions of the given quantities are:Radiation pressure $P = [M L^{-1} T^{-2}]$Radiation energy per unit area per second $Q = [M T^{-3}]$Spe

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$x = 1, y = -1, z = 1$

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(B) The dimensions of the given quantities are:Radiation pressure $P = [M L^{-1} T^{-2}]$Radiation energy per unit area per second $Q = [M T^{-3}]$Speed of light $c = [L T^{-1}]$For the expression $P^x Q^y c^z$ to be dimensionless,we have:$[M L^{-1} T^{-2}]^x [M T^{-3}]^y [L T^{-1}]^z = [M^0 L^0 T^0]$Equating the powers of $M, L,$ and $T$ on both sides:For $M: x + y = 0 \implies y = -x$For $L: -x + z = 0 \implies z = x$For $T: -2x - 3y - z = 0$Substituting $y = -x$ and $z = x$ into the $T$ equation:$-2x - 3(-x) - x = -2x + 3x - x = 0$This identity holds for any non-zero $x$. If we choose $x = 1$,then $y = -1$ and $z = 1$. Thus,the set of integers is $x = 1, y = -1, z = 1$.

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 $x, y,$ and $z$ such that $P^x Q^y c^z$ is dimensionless are:

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