JEE MAIN - Physics (2025 - 2nd April Morning Shift - No. 8)
Match List I with List II.
| List - I | List - II | ||
|---|---|---|---|
| (A) | Coefficient of viscosity | (I) | $\left[\mathrm{ML}^0 \mathrm{~T}^{-3}\right]$ |
| (B) | Intensity of wave | (II) | $\left[\mathrm{ML}^{-2} \mathrm{~T}^{-2}\right]$ |
| (C) | Pressure gradient | (III) | $\left[\mathrm{M}^{-1} \mathrm{LT}^2\right]$ |
| (D) | Compressibility | (IV) | $\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]$ |
Choose the correct answer from the options given below:
Explanation
Here are the dimensional formulas:
Coefficient of viscosity, μ
$$[\mu]=\frac{\text{pressure}\times\text{time}}{} =\frac{[M\,L^{-1}T^{-2}]\,[T]}{} =[M\,L^{-1}T^{-1}]\quad\longrightarrow\text{(IV)}$$
Intensity of a wave, I
$$[I]=\frac{\text{power}}{\text{area}} =\frac{[M\,L^2T^{-3}]}{[L^2]} =[M\,L^0T^{-3}]\quad\longrightarrow\text{(I)}$$
Pressure gradient, dP/dx
$$\left[\frac{dP}{dx}\right] =\frac{[M\,L^{-1}T^{-2}]}{[L]} =[M\,L^{-2}T^{-2}]\quad\longrightarrow\text{(II)}$$
Compressibility, κ
$$[\kappa]=\frac1{[\text{pressure}]} =[M^{-1}L\,T^2]\quad\longrightarrow\text{(III)}$$
Matching gives
(A)–(IV), (B)–(I), (C)–(II), (D)–(III), i.e. Option C.
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