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

Why concept of dimension has basic importance ?

easy

In a practical unit if the unit of mass becomes double and that of unit of time becomes half, then $8$ joule will be equal to ………….. unit of work.

medium

Let $[ {\varepsilon _0} ]$ denote the dimensional formula of the permittivity of vacuum. If $M =$ mass, $L=$ length, $T =$ time and $A=$ electric current, then:

medium

(JEE MAIN-2013)

The $SI$ unit of energy is $J=k g\, m^{2} \,s^{-2} ;$ that of speed $v$ is $m s^{-1}$ and of acceleration $a$ is $m s ^{-2} .$ Which of the formulae for kinetic energy $(K)$ given below can you rule out on the basis of dimensional arguments ( $m$ stands for the mass of the body ):

$(a)$ $K=m^{2} v^{3}$

$(b)$ $K=(1 / 2) m v^{2}$

$(c)$ $K=m a$

$(d)$ $K=(3 / 16) m v^{2}$

$(e)$ $K=(1 / 2) m v^{2}+m a$

medium

If Surface tension $(S)$, Moment of Inertia $(I)$ and Planck’s constant $(h)$, were to be taken as the fundamental units, the dimensional formula for linear momentum would be

hard

(JEE MAIN-2019)

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

Similar Questions

Why concept of dimension has basic importance ?

In a practical unit if the unit of mass becomes double and that of unit of time becomes half, then $8$ joule will be equal to ………….. unit of work.

Let $[ {\varepsilon _0} ]$ denote the dimensional formula of the permittivity of vacuum. If $M =$ mass, $L=$ length, $T =$ time and $A=$ electric current, then:

If Surface tension $(S)$, Moment of Inertia $(I)$ and Planck’s constant $(h)$, were to be taken as the fundamental units, the dimensional formula for linear momentum would be

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