Question

English

Gujarati

Hindi

1.Units, Dimensions and Measurement

hard

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

$x = y$

$x = -y$

$x = -y^2$

$y = x^2$

Solution

$\frac{M}{A t} \propto P^{x} v^{y}$

$\Rightarrow \mathrm{M} \mathrm{L}^{-2} \mathrm{T}^{-1}=\left[\mathrm{M} \mathrm{L}^{-1} \mathrm{T}^{-2}\right]^{\mathrm{x}}\left[\mathrm{L}^{1} \mathrm{T}^{-1}\right]^{\mathrm{y}}$

$=\mathrm{M}^{\mathrm{x}} \mathrm{L}^{-\mathrm{x}+\mathrm{y}} \mathrm{T}^{-2 \mathrm{x}-\mathrm{y}}$

$\mathrm{x}=1,-\mathrm{x}+\mathrm{y}=-2$ and $-2 \mathrm{x}-\mathrm{y}=-1$

From here, we get $y=-1 .$ Thus, $x=-y$

Std 11

Physics

If velocity of light $c$, Planck’s constant $h$ and gravitational constant $G$ are taken as fundamental quantities, then express time in terms of dimensions of these quantities.

medium

A calorie is a unit of heat or energy and it equals about $4.2\; J$ where $1 \;J =1\; kg \,m ^{2} \,s ^{-2}$ Suppose we employ a system of units in which the unit of mass equals $\alpha\; kg$, the unit of length equals $\beta\; m$, the unit of time is $\gamma$ $s$. Show that a calorie has a magnitude $4.2 \;\alpha^{-1} \beta^{-2} \gamma^{2}$ in terms of the new units.

medium

Time $(T)$, velocity $(C)$ and angular momentum $(h)$ are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be

hard

The dimensions of the area $A$ of a black hole can be written in terms of the universal gravitational constant $G$, its mass $M$ and the speed of light $c$ as $A=G^\alpha M^\beta c^\gamma$. Here,

hard

A neutron star with magnetic moment of magnitude $m$ is spinning with angular velocity $\omega$ about its magnetic axis. The electromagnetic power $P$ radiated by it is given by $\mu_{0}^{x} m^{y} \omega^{z} c^{u}$, where $\mu_{0}$ and $c$ are the permeability and speed of light in free space, respectively. Then,

hard

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

Solution

Similar Questions

If velocity of light $c$, Planck’s constant $h$ and gravitational constant $G$ are taken as fundamental quantities, then express time in terms of dimensions of these quantities.

Time $(T)$, velocity $(C)$ and angular momentum $(h)$ are chosen as fundamental quantities instead of mass, length and time. In terms of these, the dimensions of mass would be

The dimensions of the area $A$ of a black hole can be written in terms of the universal gravitational constant $G$, its mass $M$ and the speed of light $c$ as $A=G^\alpha M^\beta c^\gamma$. Here,