Write the dimensional formula of power. Is power a vector or scalar quantity?
(N/A) Power $(P)$ is defined as the rate of doing work or the rate of transfer of energy. Mathematically,$P = \frac{W}{t}$.
The dimensional formula of work $(W)$ is $[ML^2T^{-2}]$.
The dimensional formula of time $(t)$ is $[T]$.
Therefore,the dimensional formula of power is:
$[P] = \frac{[ML^2T^{-2}]}{[T]} = [ML^2T^{-3}]$.
Power is a scalar quantity because it is defined as the dot product of force and velocity $(P = \vec{F} \cdot \vec{v})$,and it has only magnitude,not direction.
The dimensional formula of work $(W)$ is $[ML^2T^{-2}]$.
The dimensional formula of time $(t)$ is $[T]$.
Therefore,the dimensional formula of power is:
$[P] = \frac{[ML^2T^{-2}]}{[T]} = [ML^2T^{-3}]$.
Power is a scalar quantity because it is defined as the dot product of force and velocity $(P = \vec{F} \cdot \vec{v})$,and it has only magnitude,not direction.
Explore More
Similar Questions
Given below are two statements :
Statement $(I)$ : Dimensions of specific heat are $\left[L^2 \,T^{-2} \,K^{-1}\right]$.
Statement $(II)$ : Dimensions of gas constant are $\left[ML^2 \,T^{-1} \,K^{-1}\right]$.
Statement $(I)$ : Dimensions of specific heat are $\left[L^2 \,T^{-2} \,K^{-1}\right]$.
Statement $(II)$ : Dimensions of gas constant are $\left[ML^2 \,T^{-1} \,K^{-1}\right]$.
DifficultJEE MAIN 2024
View SolutionThe physical quantities not having the same dimensions are:
MediumAIEEE 2003
View SolutionWhich of the following is dimensionless?
Easy
View SolutionForce $F = P \cos(Ax) + Q \sin(Bt)$,where $x$ and $t$ are displacement and time respectively. Which one of the following physical quantities has the dimensions of $\left[\frac{B}{A}\right]$?
Which of the following quantities can be written in $SI$ units as $kg \cdot m^2 \cdot A^{-2} \cdot s^{-3}$?
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