A physical quantity P = B²l²/m where B= magnetic induction, l= length and m = mass. The dimension of P is

The correct option is ML²T⁻⁴I⁻².

To find the dimension of the physical quantity $P=\frac{B^2{l}^2}{m}$, we can determine the dimensions of each individual variable in the formula:

1. Mass ($m$):
The dimensional formula for mass is:
$\left[m\right]=\left[M\right]$

2. Length ($l$):
The dimensional formula for length is:
$\left[l\right]=\left[L\right]$

3. Magnetic Induction ($B$):
We can find the dimensions of the magnetic field (magnetic induction) using the magnetic force formula acting on a moving charge:
$F=qvB$
Rearranging the formula for $B$:
$B=\frac{F}{qv}$
Where:
- Force $\left[F\right]=\left[ML{T}^{-2}\right]$
- Electric charge $\left[q\right]=\left[IT\right]$ (where $I$ represents electric current)
- Velocity $\left[v\right]=\left[L{T}^{-1}\right]$

Substituting these dimensions into the expression for $B$:
$\left[B\right]=\frac{\left[ML{T}^{-2}\right]}{\left[IT\right]\left[L{T}^{-1}\right]}=\left[M{T}^{-2}{I}^{-1}\right]$

4. Dimensional Formula of $P$:
Now we substitute the dimensions of $B$, $l$, and $m$ into the equation for $P$:
$\left[P\right]=\frac{{\left[B\right]}^2{\left[l\right]}^2}{\left[m\right]}$
$\left[P\right]=\frac{{\left(M{T}^{-2}{I}^{-1}\right)}^2{\left(L\right)}^2}{M}$
$\left[P\right]=\frac{M^2{T}^{-4}{I}^{-2}{L}^2}{M}$
Simplifying the powers of $M$:
$\left[P\right]=\left[M{L}^2{T}^{-4}{I}^{-2}\right]$