Verified Solution • 2025–26 Session moderate

QJEEM22Ph67f5: JEE Main 2022 Physics - Class 11 JEEM22Ph67f5 Solution: Given below are two statements : One is labelled as Assertion…

Given below are two statements : One is labelled as Assertion (A) and other is labelled as Reason (R).

Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is ρ and radius of the drop is r, then T=Kρr3/S3/2 is dimensionally correct, where K is dimensionless.

Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period.

In the light of above statements, choose the correct answer from the options given below.

Multiple Choice Options

  • A Both (A) and (R) are true and (R) is the correct explanation of (A)
  • B Both (A) and (R) are true but (R) is not the correct explanation of (A)
  • C (A) is true but (R) is false
  • D (A) is false but (R) is true

Step-by-Step Verified Solution

We know,

[S]=[MT−2][ρ]=[ML−3][r]=[L]

∴ Dimension of RHS=[M12 L−32][L32][MT−2]34=[M(12−34)L(−32+32)T64]=M−14 L0 T32

dimension of L.H.S. = [T][\mathrm{T}]

∴\therefore Dimension of LHS ≠\neq Dimension of RHS.

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