State whether the following statements are true or false:
$(a)$ $A$ physical quantity can have units but still be dimensionless.
$(b)$ Impulse and the gradient of energy have the same units.
$(c)$ The absolute error in every measurement is equal to the least count of the measuring instrument.
$(a)$ $A$ physical quantity can have units but still be dimensionless.
$(b)$ Impulse and the gradient of energy have the same units.
$(c)$ The absolute error in every measurement is equal to the least count of the measuring instrument.
(A) True. For example,plane angle is measured in radians but is dimensionless.
$(b)$ False. The unit of impulse is $N \cdot s$ (or $kg \cdot m/s$). The unit of the gradient of energy (force) is $N$ (or $kg \cdot m/s^2$). They are not the same.
$(c)$ True. By convention,the absolute error in a single measurement is taken as the least count of the measuring instrument.
$(b)$ False. The unit of impulse is $N \cdot s$ (or $kg \cdot m/s$). The unit of the gradient of energy (force) is $N$ (or $kg \cdot m/s^2$). They are not the same.
$(c)$ True. By convention,the absolute error in a single measurement is taken as the least count of the measuring instrument.
Explore More
Similar Questions
The phenomenon of physics that deals with the constitution and structure of matter at the minute scales of atoms and nuclei is
The density of water is $1000 \; kg \; m^{-3}$. The density of water vapour at $100^{\circ} C$ and $1 \; atm$ pressure is $0.6 \; kg \; m^{-3}$. The volume of a molecule multiplied by the total number gives what is called molecular volume. Estimate the volume of a water molecule.
Medium
View SolutionMatch the physical quantities given in List-$I$ with their dimensions in List-$II$.
List-$I$ List-$II$ $A$. Gravitational potential $I$. $M^0 L^2 T^{-2} K^{-1}$ $B$. Stefan's constant $II$. $M^0 L^2 T^{-2}$ $C$. Permittivity $III$. $M L^0 T^{-3} K^{-4}$ $D$. Specific heat capacity $IV$. $M^{-1} L^{-3} T^4 I^2$
$(The dimensions of mass, length, time, temperature and current are $M$, $L$, $T$, $K$ and $I$ respectively.)$
| List-$I$ | List-$II$ |
| $A$. Gravitational potential | $I$. $M^0 L^2 T^{-2} K^{-1}$ |
| $B$. Stefan's constant | $II$. $M^0 L^2 T^{-2}$ |
| $C$. Permittivity | $III$. $M L^0 T^{-3} K^{-4}$ |
| $D$. Specific heat capacity | $IV$. $M^{-1} L^{-3} T^4 I^2$ |
$(The dimensions of mass, length, time, temperature and current are $M$, $L$, $T$, $K$ and $I$ respectively.)$
If $\epsilon_0$, $E$, and $t$ represent the free space permittivity, electric field, and time respectively, then the unit of $\frac{\epsilon_0 E}{t}$ will be:
Match the List-$I$ with List-$II$. The correct match in the following is:
List-$I$
List-$II$
$A$. Boltzmann constant
$I$. $[ML^0T^0]$
$B$. Coefficient of viscosity
$II$. $[ML^{-1}T^{-1}]$
$C$. Water equivalent
$III$. $[ML^2T^{-2}K^{-1}]$
$D$. Coefficient of thermal conductivity
$IV$. $[MLT^{-3}K^{-1}]$
| List-$I$ | List-$II$ |
| $A$. Boltzmann constant | $I$. $[ML^0T^0]$ |
| $B$. Coefficient of viscosity | $II$. $[ML^{-1}T^{-1}]$ |
| $C$. Water equivalent | $III$. $[ML^2T^{-2}K^{-1}]$ |
| $D$. Coefficient of thermal conductivity | $IV$. $[MLT^{-3}K^{-1}]$ |
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo