Question
If P represents radiation pressure, E represents radiation energy striking per unit area per unit time and c represents speed of light then the possible values of non-zero integers x, y and z such that PxEycz is dimensionless, may be :
Options
Solution
[Key Concept: Radiation intensity equals radiation pressure times c, so P c/E is dimensionless.]
Dimension of
$$\begin{matrix} & \ P = \left\lbrack {ML}^{- 1}{\text{ }T}^{- 2} \right\rbrack \\ & \ E = \left\lbrack {MT}^{- 3} \right\rbrack \\ & \ c = \left\lbrack {LT}^{- 1} \right\rbrack \\ & P^{x}E^{y}c^{z} = \left\lbrack M^{x + y}{\text{ }L}^{- x + z}{\text{ }T}^{- 2x - 3y - z} \right\rbrack \\ & \left\lbrack M^{0}{\text{ }L}^{0}{\text{ }T}^{0} \right\rbrack = \left\lbrack M^{x + y}{\text{ }L}^{- x + z}{\text{ }T}^{- 2x - 3y - z} \right\rbrack \\ & \ \Rightarrow \ x + y = 0;x = z\& 2x + 3y + z = 0 \\ & 2x + 3( - x) + x = 0 \\ & x = 0;y = 0;z = 0 \end{matrix}$$
But question says x, y & z must be non-zero, so only option 'c' satisfy this.
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