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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Units and Dimensions

NTA Abhyas 2020 · Physics · Units and Dimensions

If the time period ( T ) of vibration of a liquid drop depends on...

If the time period (T)( T ) of vibration of a liquid drop depends on surface tension (S)( S ) , radius (r)( r ) of the drop and density (ρ)( ρ ) of the liquid, then the expression of TT is

Options

  1. AT=kρr3/ST = k\sqrt{ρr^{3} / S}
  2. BT=kρ1/2r3/ST = k\sqrt{{ρ}^{1 / 2} r^{3} / S}
  3. CT=kρr3/S1/2T = k\sqrt{ρr^{3} / S^{1 / 2}}
  4. DNone of these

Correct answer

A. T=kρr3/ST = k\sqrt{ρr^{3} / S}

Step-by-step solution

Let T∝SxryρzT ∝ S^{x} r^{y} {ρ}^{z} by substituting the dimension of [T]=[T][S]=[MT−2],[r]=[L],[ρ]=[ML−3][ T ] = [ T ][ S ] = [ MT^{- 2} ] , [ r ] = [ L ] , [ ρ ] = [ ML^{- 3} ] and by comparing the power of both the sides x=−1/2,y=3/2,z=1/2x = - 1 / 2, y = 3 / 2, z = 1 / 2 so T∝ρr3/S⇒T=kρr3ST ∝ \sqrt{ρr^{3} / S} ⇒ T = k\sqrt{\dfrac{ρr^{3}}{S}}
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