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JEE Main 20127 MayOnline
Exam
JEE Main
Year
2012
Date
7 May
Mode
Online
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2012 · 7 May · Online · Physics · Units and Dimensions

Given that K= energy, V= velocity, T= time. If they are chosen as...

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?

Options

  1. A[KV−2 T−2]\left[K V^{-2} \mathrm{~T}^{-2}\right]
  2. B[K2V2T−2]\left[K^2 V^2 T^{-2}\right]
  3. C[K2V−2T−2]\left[K^2 V^{-2} T^{-2}\right]
  4. D[KV2T2]\left[K V^2 T^2\right]

Correct answer

A. [KV−2 T−2]\left[K V^{-2} \mathrm{~T}^{-2}\right]

Step-by-step solution

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 =\left[K V^{-2} T^{-2}\right]
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