If pressure $P$, velocity $V$ and time $T$ are taken as fundamental physical quantities, the dimensional formula of force is
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- 1Some 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 $ORS$.View Solution
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) $(\text { volt) })^2(\mathrm{~kg})^{-1}$ - 2A travelling microscope is used to determine the refractive index of a glass slab. If $40$ divisions are there in $1 \; cm$ on main scale and $50$ Vernier scale divisions are equal to $49$ main scale divisions, then least count of the travelling microscope is $\dots \; \times 10^{-6} \; m$View Solution
- 3Match List $I$ with List $II$View Solution
List $I$ List $II$ $A$ Torque $I$ ${\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]}$ $B$ Magnetic fileld $II$ $\left[\mathrm{L}^2 \mathrm{~A}^1\right]$ $C$ Magneti moment $III$ ${\left[\mathrm{M}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]}$ $D$ permeability of free space $IV$ $\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]$ Choose the correct answer from the options given below :
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