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1.Units, Dimensions and Measurement
medium
પરિમાણરહિત રાશી $P$ ને સમીકરણ $P =\frac{\alpha}{\beta} \log _{ e }\left(\frac{ kt }{\beta x}\right)$ થી આપવામાં આવે છે; જ્યાં $\alpha$ અને $\beta$ અચળાંકો, $x$ એ અંતર; $k$ એ બોલ્ટઝમાન અચળાંક અને $t$ એ તાપમાન છે, $\alpha$ નું પરિમાણ ............. થશે.
A$[ M ^{0} L ^{-1} T ^{0} ]$
B$[ ML ^{0} T ^{-2}]$
C$[ MLT ^{-2}]$
D$[ ML ^{2} T ^{-2}]$
(JEE MAIN-2022)
Solution
$P=\frac{\alpha}{\beta} \log _{ e }\left(\frac{ kt }{\beta x }\right)$
$\frac{ kt }{\beta x }=1 \Rightarrow \beta=\frac{ kt }{ x }=\frac{ ML ^{2} T ^{-2}}{ L }$
$\left(\because E =\frac{1}{2} kt \right)$
$As \; P$ is dimensionless
$\Rightarrow[\alpha]=[\beta]=\left[ MLT ^{-2}\right]$
$\frac{ kt }{\beta x }=1 \Rightarrow \beta=\frac{ kt }{ x }=\frac{ ML ^{2} T ^{-2}}{ L }$
$\left(\because E =\frac{1}{2} kt \right)$
$As \; P$ is dimensionless
$\Rightarrow[\alpha]=[\beta]=\left[ MLT ^{-2}\right]$
Standard 11
Physics
