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1.Units, Dimensions and Measurement
medium
$K =$ ઉર્જા , $V =$ વેગ, $T =$ સમય આપેલ છે. જો તે બધા ને મૂળભૂત એકમ તરીકે લઈએ તો પૃષ્ઠતાણ નું પારિમાણિક સૂત્ર શું થાય?
A$[K\,{V^{ - 2}}{T^{ - 2}}]$
B$[K^2\,{V^2}{T^{ - 2}}]$
C$[K^2\,{V^{ - 2}}{T^{ - 2}}]$
D$[K\,{V^2}{T^2}]$
Solution
$\begin{array}{l}
Surface\,tension\, = \frac{F}{\ell } = \frac{F}{\ell } \cdot \frac{\ell }{\ell } \cdot \frac{{{T^2}}}{{{T^2}}}\\
\left( {As,F.\ell = K(energy);\frac{{{T^2}}}{{{\ell ^2}}} = {V^{ – 2}}} \right)\\
Therefore,\,surface\,tension = \left[ {K{V^{ – 2}}{T^{ – 2}}} \right]
\end{array}$
Surface\,tension\, = \frac{F}{\ell } = \frac{F}{\ell } \cdot \frac{\ell }{\ell } \cdot \frac{{{T^2}}}{{{T^2}}}\\
\left( {As,F.\ell = K(energy);\frac{{{T^2}}}{{{\ell ^2}}} = {V^{ – 2}}} \right)\\
Therefore,\,surface\,tension = \left[ {K{V^{ – 2}}{T^{ – 2}}} \right]
\end{array}$
Standard 11
Physics
