Units And Dimensions Question 4
Question 4 - 2024 (30 Jan Shift 1)
Match List-I with List-II.
| List-I | List-II | ||
|---|---|---|---|
| A. | Coefficient of viscosity | I. | $\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]$ |
| B. | Surface Tension | II. | $\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]$ |
| C. | Angular momentum | III. | $\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]$ |
| D. | Rotational kinetic energy | IV. | $\left[\mathrm{ML}^{0} \mathrm{~T}^{-2}\right]$ |
(1) A-II, B-I, C-IV, D-III
(2) A-I, B-II, C-III, D-IV
(3) A-III, B-IV, C-II, D-I
(4) A-IV, B-III, C-II, D-I
Show Answer
Answer: (3)
Solution:
$F=\eta A \frac{d v}{d y}$
$\left[M L T^{-2}\right]=\eta\left[L^{2}\right]\left[T^{-1}\right]$
$\eta=\left[M L^{-1} T^{-1}\right]$
$S . T=\frac{F}{\ell}=\frac{\left[M L T^{-2}\right]}{[L]}=\left[M L^{0} T^{-2}\right]$
$L=m v r=\left[M L^{2} T^{-1}\right]$
$K . E=\frac{1}{2} I \omega^{2}=\left[M L^{2} T^{-2}\right]$
