Given that K = energy, V = velocity, T = time. If they are chosen as the fundamental units, then what is dimensional formula for surface tension?

Question

Given that K = energy, V = velocity, T = time. If they are chosen as the fundamental units, then what is dimensional formula for surface tension? (A) [KV-2T-2] (B) [K2V2T-2] (C) [K2V-2T-2] (D) [KV2T2]

Tardigrade Admin · Accepted Answer

Surface tension =(F/ℓ)=(F/ℓ). (ℓ/ℓ). (T2/T2) (As, F.ℓ(energy); (T2/ℓ2)=V-2) Therefore, surface tension = [KV-2T-2]

Q. Given that $K =$ energy, $V =$ velocity, $T =$ time. If they are chosen as the fundamental units, then what is dimensional formula for surface tension?

$[K V^{- 2} T^{- 2}]$

$[K^{2} V^{2} T^{- 2}]$

$[K^{2} V^{- 2} T^{- 2}]$

$[K V^{2} T^{2}]$

Surface tension $= \frac{F}{ℓ} = \frac{F}{ℓ} . \frac{ℓ}{ℓ} . \frac{T ^{2}}{T ^{2}}$
$(A s, F . ℓ (e n er g y); \frac{T ^{2}}{ℓ ^{2}} = V^{- 2})$
Therefore, surface tension $= [K V^{- 2} T^{- 2}]$

Q. Given that K= energy, V= velocity, T= time. If they are chosen as the fundamental units, then what is dimensional formula for surface tension?

[KV−2T−2]

[K2V2T−2]

[K2V−2T−2]

[KV2T2]