If ${u_1}$ and ${u_2}$ are the units selected in two systems of measurement and ${n_1}$ and ${n_2}$ their numerical values, then
If ${u_1}$ and ${u_2}$ are the units selected in two systems of measurement and ${n_1}$ and ${n_2}$ their numerical values, then
- A
${n_1}{u_1} = {n_2}{u_2}$
- B
${n_1}{u_1} + {n_2}{u_2} = 0$
- C
${n_1}{n_2} = {u_1}{u_2}$
- D
$({n_1} + {u_1}) = ({n_2} + {u_2})$
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Some physical quantities are given in Column $I$ and some possible $SI$ units in which these quantities may be expressed are given in Column $II$. Match the physical quantities in Column $I$ with the units in Column $II$ and indicate your answer by darkening appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.
Column $I$
Column $II$
$(A)$ $\mathrm{GM}_e \mathrm{M}_5$
$\mathrm{G} \rightarrow$ universal gravitational constant, $\mathrm{M}_{\mathrm{e}} \rightarrow$ mass of the earth,
$\mathrm{M}_5 \rightarrow$ mass of the Sun
$(p)$ (volt) (coulomb) (metre)
$(B)$ $\frac{3 \mathrm{RT}}{\mathrm{M}} ; \mathrm{R} \rightarrow$ universal gas constant, $\mathrm{T} \rightarrow$ absolute temperature,
$\mathrm{M} \rightarrow$ molar mass
$(q)$ (kilogram) $(\text { metre) })^3$ (second) $)^{-2}$
$(C)$ $\frac{F^2}{q^2 B^2}$ ;$\quad F \rightarrow$ force, $q \rightarrow$ charge, $B \rightarrow$ magnetic field
$(r)$ $(\text { meter })^2$ (second) $)^{-2}$
$(D)$ $\frac{\mathrm{GM}_e}{\mathrm{R}_{\mathrm{e}}}, G \rightarrow$ universal gravitational constant,
$\mathrm{M}_{\mathrm{e}} \rightarrow$ mass of the earth, $\mathrm{R}_{\mathrm{e}} \rightarrow$ radius of the earth
$(s)$ (farad) $(\text { volt) })^2(\mathrm{~kg})^{-1}$
Some physical quantities are given in Column $I$ and some possible $SI$ units in which these quantities may be expressed are given in Column $II$. Match the physical quantities in Column $I$ with the units in Column $II$ and indicate your answer by darkening appropriate bubbles in the $4 \times 4$ matrix given in the $ORS$.
| Column $I$ | Column $II$ |
|
$(A)$ $\mathrm{GM}_e \mathrm{M}_5$ $\mathrm{G} \rightarrow$ universal gravitational constant, $\mathrm{M}_{\mathrm{e}} \rightarrow$ mass of the earth, $\mathrm{M}_5 \rightarrow$ mass of the Sun |
$(p)$ (volt) (coulomb) (metre) |
|
$(B)$ $\frac{3 \mathrm{RT}}{\mathrm{M}} ; \mathrm{R} \rightarrow$ universal gas constant, $\mathrm{T} \rightarrow$ absolute temperature, $\mathrm{M} \rightarrow$ molar mass |
$(q)$ (kilogram) $(\text { metre) })^3$ (second) $)^{-2}$ |
| $(C)$ $\frac{F^2}{q^2 B^2}$ ;$\quad F \rightarrow$ force, $q \rightarrow$ charge, $B \rightarrow$ magnetic field | $(r)$ $(\text { meter })^2$ (second) $)^{-2}$ |
|
$(D)$ $\frac{\mathrm{GM}_e}{\mathrm{R}_{\mathrm{e}}}, G \rightarrow$ universal gravitational constant, $\mathrm{M}_{\mathrm{e}} \rightarrow$ mass of the earth, $\mathrm{R}_{\mathrm{e}} \rightarrow$ radius of the earth |
$(s)$ (farad) $(\text { volt) })^2(\mathrm{~kg})^{-1}$ |
- [IIT 2007]