If time (t) , velocity (u) , and angular momentum (I) are taken as fundamental units. Then dimension

English

Gujarati

Hindi

1.Units, Dimensions and Measurement

medium

If time $(t)$, velocity $(u)$, and angular momentum $(I)$ are taken as the fundamental units. Then the dimension of mass $({m})$ in terms of ${t}, {u}$ and ${I}$ is

A

$[t^{-1} u^{-2}\,I^{1}]$

B

$[t^{1} u^{2}\,I^{-1}]$

C

$[t^{-2} u^{-1}\,I^{1}]$

D

$[t^{-1} u^{1}\,I^{-2}]$

(JEE MAIN-2021)

Solution

$m \propto t^{a} v^{b} \ell^{c}$

$m \propto[T]^{a}\left[L T^{-1}\right]^{b}\left[M L^{2} T^{-1}\right]^{c}$

$M^{1} L^{0} T^{0}=M^{c} L^{b+2 c} T^{a-b-c}$

comparing powers

$v=1, b=-2, a=-1$

$m \propto t^{-1} v^{-2} \ell^{1}$

Standard 11

Physics

Share

Similar Questions

The mass of a liquid flowing per second per unit area of cross section of a tube is proportional to $P^x$ and $v^y$ , where $P$ is the pressure difference and $v$ is the velocity. Then, the relation between $x$ and $y$ is

hard

Stokes' law states that the viscous drag force $F$ experienced by a sphere of radius $a$, moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$, is given by $F=6 \pi \eta a v$. If this fluid is flowing through a cylindrical pipe of radius $r$, length $l$ and pressure difference of $p$ across its two ends, then the volume of water $V$ which flows through the pipe in time $t$ can be written as $\frac{V}{t}=k\left(\frac{p}{l}\right)^a \eta^b r^c$, where $k$ is a dimensionless constant. Correct values of $a, b$ and $c$ are

hard

(KVPY-2017)

If ${E}, {L}, {m}$ and ${G}$ denote the quantities as energy, angular momentum, mass and constant of gravitation respectively, then the dimensions of ${P}$ in the formula ${P}={EL}^{2} {m}^{-5} {G}^{-2}$ are

medium

(JEE MAIN-2021)

The value of gravitational acceleration $C.G.S.$ system is $980 \;cm / sec$ ? .find the value of $g$ in $M.K.S$ system?

easy

In the expression $P = El^2m^{-5}G^{-2}$, $E$, $l$, $m$ and $G$ denote energy, mass, angular momentum and gravitational constant respectively. Show that $P$ is a dimensionless quantity.

medium