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1.Units, Dimensions and Measurement
hard
If the speed of light $(c)$, acceleration due to gravity $(g)$ and pressure $(p)$ are taken as the fundamental quantities, then the dimension of gravitational constant is
A
${c^2}{g^0}{p^{ - 2}}$
B
${c^0}{g^2}{p^{ - 1}}$
C
$c{g^3}{p^{ - 2}}$
D
${c^{ - 1}}{g^0}{p^{ - 1}}$
Solution
(b) Let $[G] \propto {c^x}{g^y}{p^z}$
by substituting the following dimensions :
$[G] = [{M^{ – 1}}{L^3}{T^{ – 2}}],\,[c] = [L{T^{ – 1}}],[g] = [L{T^{ – 2}}]$
$[p] = [M{L^{ – 1}}{T^{ – 2}}]$
and by comparing the powers of both sides we can get $x = 0,\,y = 2,\,z = – 1$
$\therefore $ $[G] \propto {c^0}{g^2}{p^{ – 1}}$
Standard 11
Physics
