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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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