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

[E^-2 V^-1 T^-3]

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[E V^-2 T^-1]

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[EV^-1T^-2]

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[EV^-2T^-2]

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Solution

The correct option is D
[EV^-2T^-2]

[Surface Tension] = $M T^{- 2}$

$∴ M T^{- 2} = K E^{a} V^{b} T^{c}$

$= k (M L^{2} T^{2})^{a} (L T^{1}) b T^{c}$
$M T^{- 2} = K M^{a} L^{2 a + b} T^{- 2 a - b + c}$
$∴ a = 1$

2a + b = 0

-2a – b + c = -2

On solving a = 1, b = -2 , c = - 2

$∴$ Required answer is $E V^{- 2} T^{- 2}$

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