If P represents radiation pressure, c represents speed of light and Q represents radiation energy st

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1.Units, Dimensions and Measurement

hard

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 $x,\,y$ 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

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

(AIPMT-1992)

Solution

(b) By substituting the dimension of given quantities

${[M{L^{ – 1}}{T^{ – 2}}]^x}{[M{T^{ – 3}}]^y}{[L{T^{ – 1}}]^z} = {[MLT]^0}$

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 $(b).$

Standard 11

Physics

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