$\begin{aligned} \text{Match List-I with List-II.} \\ \begin{array}{llll} & \text{List-I} & & \text{List-II}…

$\begin{aligned} \text{Match List-I with List-II.} \\ \begin{array}{llll} & \text{List-I} & & \text{List-II} \\ \text{A.} & \text{Coefficient of viscosity} & \text{I.} & [M L^{2} T^{-2}] \\ \text{B.} & \text{Surface Tension} & \text{II.} & [M L^{2} T^{-1}] \\ \text{C.} & \text{Angular momentum} & \text{III.} & [M L^{-1} T^{-1}] \\ \text{D.} & \text{Rotational kinetic energy} & \text{IV.} & [M L^{0} T^{-2}] \\ \end{array} \end{aligned}$
  1. A-II, B-I, C-IV, D-III
  2. A-I, B-II, C-III, D-IV
  3. A-III, B-IV, C-II, D-I
  4. A-IV, B-III, C-II, D-I

Solution

Viscous force is given by, F=ηAdvdy.

Hence, MLT-2=ηL2T-1

⇒η=ML-1T-1

Surface tension is given by, ST=Fℓ.

Hence, dimension will be =MLT-2[L]=ML0T-2

Angular momentum, L=mvr=ML2T-1

Rotational kinetic energy, K.E=12Iω2=ML2T-2

Asked in: JEE Main 2024 (30 Jan Shift 1)

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