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JEE Main 20204 SeptemberEvening Shift
Exam
JEE Main
Year
2020
Date
4 September
Shift
Evening Shift
Subject
Physics
Chapter
Units and Dimensions

JEE Main 2020 · 4 September · Evening Shift · Physics · Units and Dimensions

A quantity x is given by ( 1F v ^ 2 / W L ^ 4 ) in terms of moment...

A quantity xx is given by (1Fv2/WL4)( 1F{v}^{2} / W{L}^{4} ) in terms of moment of inertia II, force FF, velocity vv, work WW and length LL. The dimensional formula for xx is same as that of :

Options

  1. Aplanck's constant
  2. Bforce constant
  3. Cenergy density
  4. Dcoefficient of viscosity

Correct answer

C. energy density

Step-by-step solution

IFv2WL4=(M1L2)(M+L1T−2)(L1T−2)2(M1L2T−2)(L4)=M1L−2T−2L3=M4L−1T−2=\dfrac{{IFv}^{2}}{{WL}^{4}} = \dfrac{\left({M}^{1}{L}^{2}\right)\left({M}^{+}{L}^{1}{T}^{- 2}\right){\left({L}^{1}{T}^{- 2}\right)}^{2}}{\left({M}^{1}{L}^{2}{T}^{- 2}\right)\left({L}^{4}\right)} = \dfrac{{M}^{1}{L}^{- 2}{T}^{- 2}}{{L}^{3}} = {M}^{4}{L}^{- 1}{T}^{- 2} = Energy density
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