If energy (E), velocity (V) and time (T) are chosen as fundamental quantities, dimensional formula o

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1.Units, Dimensions and Measurement

hard

If energy $(E),$ velocity $(V)$ and time $(T)$ are chosen as the fundamental quantities, the dimensional formula of surface tension will be

A

$[EV^{-2}T^{-1}]$

B

$[EV^{-1}T^{-2}]$

C

$[EV^{-2}T^{-2}]$

D

$[E^{-2} V^{-1}T^{-3}]$

(AIPMT-2015) (AIEEE-2012)

Solution

$S = E ^{ x } V ^{ y } T ^{ z }$

$S = \frac FL$ $\Rightarrow[ T ]=\left[ MT ^{-2}\right]$

$[ E ]=\left[ ML ^2 T ^{-2}\right]$

${[ V ]=\left[ LT ^{-1}\right] }$

${[ T ]=[ T ] }$

${\left[ MT { }^{-2}\right]=\left[ E ^{ x } V ^{ y } t ^{ z }\right]=\left[ ML ^2 T ^{-2}\right]^{ x }\left[ LT ^{-1}\right]^{ y }[ T ]^{ z } }$

Comparing coefficients

$x=1$

$2 x+y=0$

$-2 x-y+z=-2$

Solving above equations $x =1, y =-2, z =-2$

Substituting in expression of surface tension:

$S = EV ^{-2} T ^{-2}$

Standard 11

Physics

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