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If P represents radiation Pressure, C represents speed of light and Q represents radiation energy striking 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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$x = 1, y = - 1, z = 1$

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

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

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

answer is B.

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Detailed Solution

$[P] = [{ML}^{- 1} T^{- 2}]; [C] = [{LT}^{- 1}]; [Q] = \frac{[{ML}^{2} T^{- 2}]}{[L^{2} T^{1}]} = [{ML}^{0} T^{- 3}]$

$Given : [M^{0} L^{0} T^{0}] = {[P]}^{x} {[Q]}^{y} {[C]}^{z}$

$\Rightarrow M^{0} L^{0} T^{0} = M^{x + y} L^{- x + z} T^{- 2 x - 3 y - z}$

$Comparing power, x + y = 0 - x + z = 0, - 2 x - 3 y - z = 0$

$Above three will be satisfied when, x = 1, y = - 1, z = 1$

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