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1.Units, Dimensions and Measurement
hard
ફોટોઇલેક્ટ્રિક અસરમાં રહેલ સ્ટોપિંગ પોટેન્શીયલ $\mathrm{V}_{0}$ નું પરિમાણ પ્લાન્કના અચળાંક $h$, પ્રકાશનો વેગ $c$, ગુરુત્વાકર્ષણનો અચળાંક $G$ અને વિદ્યુતપ્રવાહ $A$ ના સ્વરૂપમાં કેવી રીતે દર્શાવાય?
A$\mathrm{h}^{2} \mathrm{G}^{3 / 2} \mathrm{C}^{1 / 3} \mathrm{A}^{-1}$
B$\mathrm{h}^{-2 / 3} \mathrm{c}^{-1 / 3} \mathrm{G}^{4 / 3} \mathrm{A}^{-1}$
C$\mathrm{h}^{1 / 3} \mathrm{G}^{2 / 3} \mathrm{c}^{1 / 3} \mathrm{A}^{-1}$
D$\mathrm{h}^{0} \mathrm{c}^{5} \mathrm{G}^{-1} \mathrm{A}^{-1}$
(JEE MAIN-2020)
Solution
$\mathrm{v}_{0}=\mathrm{h}^{\mathrm{x}} \mathrm{c}^{\mathrm{y}} \mathrm{G}^{\mathrm{z}} \mathrm{A}^{\mathrm{w}}$
$\frac{\mathrm{ML}^{2} \mathrm{T}^{-2}}{\mathrm{AT}}=\left(\mathrm{ML}^{2} \mathrm{T}^{-1}\right)^{\mathrm{x}}\left(\mathrm{LT}^{-1}\right)^{\mathrm{y}}\left(\mathrm{M}^{-1} \mathrm{L}^{3} \mathrm{T}^{-2}\right)^{\mathrm{z}} \mathrm{A}^{\mathrm{w}}$
$\Rightarrow \mathrm{w}=-1$
$(\mathrm{x}-\mathrm{z}=1)$
$(\mathrm{x}-\mathrm{z}=1)$
$-\mathrm{x}-\mathrm{x}=1-2 \mathrm{z}=2$
$-\mathrm{x}-\mathrm{y}-2 \mathrm{z}=-3$
$\mathrm{x}-\frac{1}{2} \mathrm{x}=0$
$\mathrm{x}=0$
$\mathrm{x}=-1$
$2 \times 0+\mathrm{y}+3 \mathrm{x}-1=2$
$y=5$
$\Rightarrow \mathrm{v}_{0}=\mathrm{h}^{0} \mathrm{c}^{5} \mathrm{G}^{-1} \mathrm{A}^{-1}$
$\frac{\mathrm{ML}^{2} \mathrm{T}^{-2}}{\mathrm{AT}}=\left(\mathrm{ML}^{2} \mathrm{T}^{-1}\right)^{\mathrm{x}}\left(\mathrm{LT}^{-1}\right)^{\mathrm{y}}\left(\mathrm{M}^{-1} \mathrm{L}^{3} \mathrm{T}^{-2}\right)^{\mathrm{z}} \mathrm{A}^{\mathrm{w}}$
$\Rightarrow \mathrm{w}=-1$
$(\mathrm{x}-\mathrm{z}=1)$
$(\mathrm{x}-\mathrm{z}=1)$
$-\mathrm{x}-\mathrm{x}=1-2 \mathrm{z}=2$
$-\mathrm{x}-\mathrm{y}-2 \mathrm{z}=-3$
$\mathrm{x}-\frac{1}{2} \mathrm{x}=0$
$\mathrm{x}=0$
$\mathrm{x}=-1$
$2 \times 0+\mathrm{y}+3 \mathrm{x}-1=2$
$y=5$
$\Rightarrow \mathrm{v}_{0}=\mathrm{h}^{0} \mathrm{c}^{5} \mathrm{G}^{-1} \mathrm{A}^{-1}$
Standard 11
Physics
