Which of the following units denotes the dimensions [ML2/Q2] , where Q denotes the electric charge?

Question

Which of the following units denotes the dimensions [ML2/Q2] , where Q denotes the electric charge? (A) Wb/m2 (B) henry (H). (C) H/m2 (D) weber (Wb)

Tardigrade Admin · Accepted Answer

Weber = ML 2 T -2 I -1 = ML 2 T -2 Q -1 T = ML 2 T -1 Q -1 ( I = QT -1) Henry H is SI unit of inductance. H = ML 2 T -2 I -2 also I = QT -1 so H = ML 2 T -2 Q -2 T 2 = ML 2 Q -2

Q. Which of the following units denotes the dimensions $[M L^{2} / Q^{2}]$ , where Q denotes the electric charge?

$Wb / m^{2}$

henry (H).

$H / m^{2}$

weber (Wb)

Weber $= M L^{2} T^{- 2} I^{- 1}$
$= M L^{2} T^{- 2} Q^{- 1} T$
$= M L^{2} T^{- 1} Q^{- 1}$
$(I = Q T^{- 1})$
Henry $H$ is SI unit of inductance.
$H = M L^{2} T^{- 2} I^{- 2}$
also $I = Q T^{- 1}$
so $H = M L^{2} T^{- 2} Q^{- 2} T^{2}$
$= M L^{2} Q^{- 2}$

Q. Which of the following units denotes the dimensions [ML2/Q2] , where Q denotes the electric charge?

Wb/m2