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1.Units, Dimensions and Measurement
medium
$v$ વેગ, $A$ પ્રવેગ અને $F$ બળ હોય,તો કોણીય વેગમાનનું પારિમાણીક સૂત્ર શું થશે?
A
$ F{A^{ - 1}}v $
B
$ F{v^3}{A^{ - 2}} $
C
$ F{v^2}{A^{ - 1}} $
D
$ {F^2}{v^2}{A^{ - 1}} $
Solution
(b) $L \propto {v^x}{A^y}{F^z}$ $ \Rightarrow $ $L = k{v^x}{A^y}{F^z}$
Putting the dimensions in the above relation
$[M{L^2}{T^{ – 1}}] = k{[L{T^{ – 1}}]^x}{[L{T^{ – 2}}]^y}{[ML{T^{ – 2}}]^z}$
$⇒$ $[M{L^2}{T^{ – 1}}] = k[{M^z}{L^{x + y + z}}{T^{ – x – 2y – 2z}}]$
Comparing the powers of $M,\,L$ and $T$
$z = 1$ …$(i)$
$x + y + z = 2$ …$(ii)$
$ – x – 2y – 2z = – 1$ …$(iii)$
On solving $(i)$, $(ii)$ and $(iii)$ $x = 3,\,y = – 2,\,z = 1$
So dimension of $L$ in terms of $v,\,A$ and $f$
$[L] = [F{v^3}{A^{ – 2}}]$
Standard 11
Physics
