Medium
State whether the following statements are true or false:
$(a)$ $A$ dimensionally incorrect equation can be correct.
$(b)$ $1 \ AU = 9.46 \times 10^{15} \ m$
$(c)$ The dimensional formula of force and stress are the same.
$(d)$ The dimensions of a physical quantity are different in different systems of units.
$(a)$ $A$ dimensionally incorrect equation can be correct.
$(b)$ $1 \ AU = 9.46 \times 10^{15} \ m$
$(c)$ The dimensional formula of force and stress are the same.
$(d)$ The dimensions of a physical quantity are different in different systems of units.
(NONE) False. $A$ dimensionally incorrect equation must be physically incorrect.
$(b)$ False. $1 \ AU = 1.496 \times 10^{11} \ m$. The value $9.46 \times 10^{15} \ m$ represents $1 \ \text{light year}$.
$(c)$ False. The dimensional formula of force is $[M^1 L^1 T^{-2}]$, while the dimensional formula of stress (force per unit area) is $[M^1 L^{-1} T^{-2}]$.
$(d)$ False. The dimensions of a physical quantity are independent of the system of units used; only the numerical value changes.
$(b)$ False. $1 \ AU = 1.496 \times 10^{11} \ m$. The value $9.46 \times 10^{15} \ m$ represents $1 \ \text{light year}$.
$(c)$ False. The dimensional formula of force is $[M^1 L^1 T^{-2}]$, while the dimensional formula of stress (force per unit area) is $[M^1 L^{-1} T^{-2}]$.
$(d)$ False. The dimensions of a physical quantity are independent of the system of units used; only the numerical value changes.
Explore More
Similar Questions
Match the following physical quantities in $LIST$-$I$ with their dimensional formulas in $LIST$-$II$:
$LIST$-$I$ $LIST$-$II$ $A$. Planck's constant $I$. $ML^2T^{-2}$ $B$. Stopping potential $II$. $T^{-1}$ $C$. Work function $III$. $ML^2T^{-1}$ $D$. Threshold frequency $IV$. $ML^2T^{-3}A^{-1}$
| $LIST$-$I$ | $LIST$-$II$ |
| $A$. Planck's constant | $I$. $ML^2T^{-2}$ |
| $B$. Stopping potential | $II$. $T^{-1}$ |
| $C$. Work function | $III$. $ML^2T^{-1}$ |
| $D$. Threshold frequency | $IV$. $ML^2T^{-3}A^{-1}$ |
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 SolutionThe maximum percentage errors in the measurement of mass $(M)$,radius $(R)$,and angular velocity $(\omega)$ of a ring are $2 \%$,$1 \%$,and $1 \%$ respectively. Find the maximum percentage error in the measurement of its rotational kinetic energy $(K = \frac{1}{2} I \omega^{2})$. (in $\%$)
Medium
View SolutionIdentify the incorrect statement.
Fill in the blanks:
$(a)$ The volume of a cube of side $1\; cm$ is equal to $\ldots \ldots\, m ^{3}$
$(b)$ The surface area of a solid cylinder of radius $2.0 \;cm$ and height $10.0\; cm$ is equal to $\ldots(mm)^{2}$
$(c)$ $A$ vehicle moving with a speed of $18\; km\, h ^{-1}$ covers $\ldots ..m$ in $1\; s$
$(d)$ The relative density of lead is $11.3$. Its density is $\ldots ..\, g\, cm ^{-3}$ or $\ldots . .\, kg\, m ^{-3}$.
$(a)$ The volume of a cube of side $1\; cm$ is equal to $\ldots \ldots\, m ^{3}$
$(b)$ The surface area of a solid cylinder of radius $2.0 \;cm$ and height $10.0\; cm$ is equal to $\ldots(mm)^{2}$
$(c)$ $A$ vehicle moving with a speed of $18\; km\, h ^{-1}$ covers $\ldots ..m$ in $1\; s$
$(d)$ The relative density of lead is $11.3$. Its density is $\ldots ..\, g\, cm ^{-3}$ or $\ldots . .\, kg\, m ^{-3}$.
Easy
View SolutionVedclass 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