Embibe Experts Solutions for Chapter: Unit & Dimension, Exercise 1: Exercise

The dimensions of Stefan-Boltzmann constant $\sigma$ can be written in terms of Planck's constant $h$, Boltzmann constant $K_B$ and the speed of light $c$ as $\sigma =h^{\alpha }{K}_B{}^{\beta }c^{\gamma }.$ Here

In an experiment, the mass of an object is measured by applying a known force on it, and then measuring its acceleration. If in the experiment, the measured values of applied force and the measured acceleration are $F=10.0\pm 0.2 \mathrm{N}$ and $a=1.00\pm 0.01 \mathrm{m} {\mathrm{s}}^{-2}$ respectively, the mass of the object is

Stoke's law states that the viscous drag force F experience by a sphere of radius a, moving with a speed v through a fluid with coefficient of  viscosity $\eta ,$ is given by $F=6\pi \eta av$. If this fluid is flowing through a cylindrical pipe of radius r, length $I$ and a 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

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

The length and width of a rectangular room are measured to be $3.95\pm 0.05 \mathrm{m}$ and $3.05\pm 0.05 \mathrm{m}$, respectively. The area of the floor is

Stoke's law states that the viscous drag force experienced by a sphere of radius $a$, moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$, is given by $\mathrm{F}=6\pi \eta Rv$. If the fluid is flowing through a cylindrical pipe of radius $r,$ length $l,$ and the 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

Force $\overrightarrow{\mathrm{F}}$ applied on a body is written as $\overrightarrow{F}=(\hat{n}\times \hat{F})·\hat{n}+\overrightarrow{G},$ where $\hat{n}$ is a unit vector. The vector $\overrightarrow{G}$ is equal to

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 ${\mu }_0^x{m}^y{\omega }^2{c}^u,$ where ${\mu }_n$ and $c$ are the permeability and speed of light in free space, respectively. Then