JEE Main 2026 Apr 8 Shift 2, Physics Q2: Units And Dimensions

$[H]=\mathrm{I}{\mathrm{L}}^{-1}$, $[E]=\mathrm{M}\mathrm{L}{\mathrm{I}}^{-1}{\mathrm{T}}^{-3}$, $[ϵ]={\mathrm{M}}^{-1}{\mathrm{L}}^{-3}{\mathrm{I}}^2{\mathrm{T}}^4$, $[x]=\mathrm{L}$, $[t]=\mathrm{T}$.

Equating exponents of $\mathrm{M},\mathrm{L},\mathrm{I},\mathrm{T}$ on both sides of $\mathrm{I}{\mathrm{L}}^{-1}={\mathrm{L}}^p({\mathrm{M}}^{-1}{\mathrm{L}}^{-3}{\mathrm{I}}^2{\mathrm{T}}^4{)}^q(\mathrm{ML}{\mathrm{I}}^{-1}{\mathrm{T}}^{-3}{)}^r{\mathrm{T}}^{-s}$:

$\mathrm{M}:-q+r=0$

$\mathrm{L}:p-3q+r=-1$

$\mathrm{I}:2q-r=1$

$\mathrm{T}:4q-3r-s=0$

Solving: $q=1,r=1,p=1,s=1$.

$\therefore$ $(p,q,r,s)=(1,1,1,1)$.