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

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$M L T^{- 3}$

$M L^{2} T^{- 4} I^{- 2}$

$M^{2} L^{2} T^{- 4} I$

$M L T^{- \hat{2}} I^{- \hat{2}}$

answer is B.

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Detailed Solution

$F = B I L$

$∴$ Dimension of $[B] = \frac{[F]}{[I] [L]} = \frac{[M L T^{- 2}]}{[I] [L]}$

$= [M T^{- 2} I^{- 1}]$

Now dimension of $[P] = \frac{B^{2} l^{2}}{m}$

$\begin{aligned} = \frac{{[M T^{- 2} I^{- 1}]}^{2} \times [L^{2}]}{[M]} \\ = [M L^{2} T^{- 4} I^{- 2}] \end{aligned}$

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