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1.Units, Dimensions and Measurement
hard
Match List $-I$ with List $-II$
| List $-I$ | List $-II$ | ||
| $A$. | Coefficient of Viscosity | $I$. | $[M L^2T^{–2}]$ |
| $B$. | Surface Tension | $II$. | $[M L^2T^{–1}]$ |
| $C$. | Angular momentum | $III$. | $[M L^{-1}T^{–1}]$ |
| $D$. | Rotational Kinetic energy | $IV$. | $[M L^0T^{–2}]$ |
A$ A-II, B-I, C-IV, D-III$
B$ A-I, B-II, C-III, D-IV$
C$ A-III, B-IV, C-II, D-I$
D$A-IV, B-III, C-II, D-I$
(JEE MAIN-2024)
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]$
$ {\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]$
Standard 11
Physics
Similar Questions
Match List$-I$ with List$-II.$
| List$-I$ | List$-II$ |
| $(a)$ Capacitance, $C$ | $(i)$ ${M}^{1} {L}^{1} {T}^{-3} {A}^{-1}$ |
| $(b)$ Permittivity of free space, $\varepsilon_{0}$ | $(ii)$ ${M}^{-1} {L}^{-3} {T}^{4} {A}^{2}$ |
| $(c)$ Permeability of free space, $\mu_{0}$ | $(iii)$ ${M}^{-1} L^{-2} T^{4} A^{2}$ |
| $(d)$ Electric field, $E$ | $(iv)$ ${M}^{1} {L}^{1} {T}^{-2} {A}^{-2}$ |
