Units & Dimensions

JEE Main level, single correct, medium

141 of 149

Question 141 of 149

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

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Answer: (A) [KV−2 T−2]\left[K V^{-2} \mathrm{~T}^{-2}\right]

Surface tension =Fℓ=Fℓ⋅ℓℓ⋅T2T2=\frac{F}{\ell}=\frac{F}{\ell} \cdot \frac{\ell}{\ell} \cdot \frac{T^2}{T^2} (As, F.ℓ=K(F . \ell=K\left(\right. energy) ;T2ℓ2=V−2; \frac{T^2}{\ell^2}=V^{-2} ) Therefore, surface tension =[KV−2T−2]=\left[K V^{-2} T^{-2}\right]

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