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Question: A physical quantity \(P = \frac{B^{2}l^{2}}{m}\) where B= magnetic induction, l= length and m = mass...

A physical quantity P=B2l2mP = \frac{B^{2}l^{2}}{m} where B= magnetic induction, l= length and m = mass. The dimension of P is

A

MLT−3MLT^{- 3}

B

ML2T−4ML^{2}T^{- 4}I–2

C

M2L2T−4IM^{2}L^{2}T^{- 4}I

D

MLT−2I−2MLT^{- 2}I^{- 2}

Answer

ML2T−4ML^{2}T^{- 4}I–2

Explanation

Solution

F = BIL ∴Dimensionof[B]=[F][I][L]=[MLT−2][I][L]\therefore\text{Dimensionof}\lbrack B\rbrack = \frac{\lbrack F\rbrack}{\lbrack I\rbrack\lbrack L\rbrack} = \frac{\lbrack MLT^{- 2}\rbrack}{\lbrack I\rbrack\lbrack L\rbrack}=

[MT−2I−1]\lbrack MT^{- 2}I^{- 1}\rbrack

Now dimension of [P]=B2l2m=[MT−2I−1]2×[L2][M]\lbrack P\rbrack = \frac{B^{2}l^{2}}{m} = \frac{\lbrack MT^{- 2}I^{- 1}\rbrack^{2} \times \lbrack L^{2}\rbrack}{\lbrack M\rbrack}

=[ML2T−4I−2]= \lbrack ML^{2}T^{- 4}I^{- 2}\rbrack