Physics - Unit & Dimension Question with Solution | TestHub

(A) Pressure gradient is stated as $\frac{dP}{dx}=\frac{F}{Al}=\frac{\left[{\mathrm{MLT}}^{-2}\right]}{\left[{\mathrm{L}}^2\right]\left[\mathrm{L}\right]}=\left[{\mathrm{M}}^1{\mathrm{L}}^{-2}{\mathrm{T}}^{-2}\right]$   (III)

(B) Energy density is stated as $u=\frac{\mathrm{Energy}}{\mathrm{Volume}}=\frac{\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]}{\left[{\mathrm{L}}^3\right]}=\left[{\mathrm{M}}^1{\mathrm{L}}^{-1}{\mathrm{T}}^{-2}\right]$   (II)

(C) Electric field is stated as $E=\frac{\mathrm{Force}}{\mathrm{Charge}}=\frac{\left[{\mathrm{MLT}}^{-2}\right]}{\left[\mathrm{AT}\right]}=\left[{\mathrm{M}}^1{\mathrm{L}}^1{\mathrm{T}}^{-3}{\mathrm{A}}^{-1}\right]$   (IV)

(D) Latent heat is stated as $L=\frac{\mathrm{Heat}}{\mathrm{Mass}}=\frac{\mathrm{Energy} }{\mathrm{Mass}}=\frac{\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]}{\left[\mathrm{M}\right]}=\left[{\mathrm{M}}^0{\mathrm{L}}^2{\mathrm{T}}^{-2}\right]$     (I)