JEE Main 2023 — Units and Dimensions Question with Solution

(A) Young's modulus is stated as$\mathrm{Y}=\frac{\mathrm{Stress}}{\mathrm{Strain}}=\frac{{\displaystyle \frac{F}{A}}}{{\displaystyle \frac{∆l}{l}}}=\frac{Fl}{A∆l}=\frac{\left[{\mathrm{MLT}}^{-2}\right]\left[\mathrm{L}\right]}{\left[{\mathrm{L}}^2\right]\left[\mathrm{L}\right]}=\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-2}\right]$(B) Coefficient of viscosity is stated as $\eta =\frac{F}{6\pi rv}$, here, $v$ is velocity.

$\left(\eta \right)=\frac{\left[{\mathrm{MLT}}^{-2}\right]}{\left[\mathrm{L}\right]\left[{\mathrm{LT}}^{-1}\right]}=\left[{\mathrm{ML}}^{-1}{\mathrm{T}}^{-1}\right]$

(C) Planck's Constant is stated as $h=\frac{\text{Energy}}{\text{Frequency}}=\frac{\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]}{\left[{\mathrm{T}}^{-1}\right]}=\left[{\mathrm{ML}}^2{\mathrm{T}}^{-1}\right]$

(D) Work function has the same dimension as that of energy, so $\left[\varphi \right]=\left[{\mathrm{ML}}^2{\mathrm{T}}^{-2}\right]$

Thus, A-III, B-I, C-II, D-IV