Q46 / 92 · NTA Abhyas (JEE Main) 2020 · Physics · Units and Dimensions

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

  • Correct answer
    A
    T=k ρ r 3 /S
  • B
    T=k ρ 1/2 r 3 /S
  • C
    T=k ρ r 3 / S 1/2
  • D
    None of these

Solution

Let T∝ S x r y ρ z by substituting the dimension of [T]=[T] [S]=[M T −2 ], [r]=[L], [ρ]=[M L −3 ] and by comparing the power of both the sides x=−1/2, y=3/2, z=1/2 so T∝ ρ r 3 /S ⇒T=k ρ r 3 S

Hence, the correct answer is option: 'A'.

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