A quantity f is given by f=√{frac{{hc}^{5}}{{G}}} where c is speed of light, G universal gravitati

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1.Units, Dimensions and Measurement

medium

A quantity $f$ is given by $f=\sqrt{\frac{{hc}^{5}}{{G}}}$ where $c$ is speed of light, $G$ universal gravitational constant and $h$ is the Planck's constant. Dimension of $f$ is that of

Momentum

Area

Energy

Volume

(JEE MAIN-2020)

Solution

$[\mathrm{h}]=\mathrm{M}^{1} \mathrm{L}^{2} \mathrm{T}^{-1}$

$[\mathrm{C}]=\mathrm{L}^{1} \mathrm{T}^{-1}$

$[\mathrm{G}]=\mathrm{M}^{-1} \mathrm{L}^{3} \mathrm{T}^{-2}$

$[\mathrm{f}]=\sqrt{\frac{\mathrm{M}^{1} \mathrm{L}^{2} \mathrm{T}^{-1} \times \mathrm{L}^{5} \mathrm{T}^{-5}}{\mathrm{M}^{-1} \mathrm{L}^{3} \mathrm{T}^{-2}}}=\mathrm{M}^{1} \mathrm{L}^{2} \mathrm{T}^{-2}$

Standard 11

Physics

The density of a material is $CGS$ system of units is $4\,g/cm^3$. In a system of units in which unit of length is $10\,cm$ and unit of mass is $100\,g$, the value of density of material will be

medium

Match List $I$ with List $II$ and select the correct answer using the codes given below the lists :

List $I$ List $II$

$P.$ Boltzmann constant $1.$ $\left[ ML ^2 T ^{-1}\right]$

$Q.$ Coefficient of viscosity $2.$ $\left[ ML ^{-1} T ^{-1}\right]$

$R.$ Planck constant $3.$ $\left[ MLT ^{-3} K ^{-1}\right]$

$S.$ Thermal conductivity $4.$ $\left[ ML ^2 T ^{-2} K ^{-1}\right]$

Codes: $ \quad \quad P \quad Q \quad R \quad S $

hard

(IIT-2013)

The potential energy of a particle varies with distance $x$ from a fixed origin as $V = \frac{{A\sqrt x }}{{x + B}}$,where
$A$ and $B$ are constants. The dimensions of $AB$ are

hard

(AIIMS-2017)

A spherical body of mass $m$ and radius $r$ is allowed to fall in a medium of viscosity $\eta $. The time in which the velocity of the body increases from zero to $0.63$ times the terminal velocity $(v)$ is called time constant $(\tau )$. Dimensionally $\tau $ can be represented by

medium

(AIIMS-1987)

The density of a material in $CGS$ system of units is $4\, g\, cm^{-3}$ . In a system of units in which unit of length is $10\, cm$ and unit of mass is $100 \,g,$ the value of density of material will be

medium

(AIPMT-2011)

List $I$	List $II$
$P.$ Boltzmann constant	$1.$ $\left[ ML ^2 T ^{-1}\right]$
$Q.$ Coefficient of viscosity	$2.$ $\left[ ML ^{-1} T ^{-1}\right]$
$R.$ Planck constant	$3.$ $\left[ MLT ^{-3} K ^{-1}\right]$
$S.$ Thermal conductivity	$4.$ $\left[ ML ^2 T ^{-2} K ^{-1}\right]$

A quantity $f$ is given by $f=\sqrt{\frac{{hc}^{5}}{{G}}}$ where $c$ is speed of light, $G$ universal gravitational constant and $h$ is the Planck's constant. Dimension of $f$ is that of

Solution

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The potential energy of a particle varies with distance $x$ from a fixed origin as $V = \frac{{A\sqrt x }}{{x + B}}$,where
$A$ and $B$ are constants. The dimensions of $AB$ are