The position of a particle moving on the x-ax | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The principle of homogeneity of dimensions states that only quantities with the same dimensions can be added or subtracted. Since $x(t)$ represent

Vedclass · Accepted Answer

$L^2 T^{-2}$

Vedclass · Answer

(C) The principle of homogeneity of dimensions states that only quantities with the same dimensions can be added or subtracted. Since $x(t)$ represents position,its dimension is $[L]$.$1$. For the term $A \sin t$: The argument of a trigonometric function must be dimensionless. Thus,$[A] = [x] = [L]$.$2$. For the term $B \cos^2 t$: Similarly,$[B] = [x] = [L]$.$3$. For the term $Ct^2$: Since $[Ct^2] = [x] = [L]$,we have $[C] [T^2] = [L]$,which implies $[C] = [L T^{-2}]$.$4$. For the term $D$: Since $D$ is added to $x(t)$,$[D] = [x] = [L]$.Now,calculate the dimension of $\frac{ABC}{D}$:$\left[ \frac{ABC}{D} ight] = \frac{[L] 	imes [L] 	imes [L T^{-2}]}{[L]} = [L^2 T^{-2}]$.

The position of a particle moving on the $x-$axis is given by $x(t) = A \sin t + B \cos^2 t + Ct^2 + D$,where $t$ is time. The dimension of $\frac{ABC}{D}$ is $-$

Similar Questions

The equation of state of some gases can be expressed as $(P + \frac{a}{V^2}) = \frac{b\theta}{l}$,where $P$ is the pressure,$V$ is the volume,$\theta$ is the absolute temperature,and $a$ and $b$ are constants. The dimensional formula of $a$ is

In the relation $y = a \cos (\omega t - kx)$,the dimensional formula for $k$ is

$L$, $C$, and $R$ represent the physical quantities inductance, capacitance, and resistance, respectively. The dimensional formula $ML^2T^{-4}A^{-2}$ corresponds to . . . . . . .

$A$ charged particle of charge $e$ and mass $m$ is moving in an electric field $\vec{E}$ and magnetic field $\vec{B}$. Construct dimensionless quantities and quantities of dimension $T^{-1}$.

Given that $K =$ energy,$V =$ velocity,$T =$ time. If they are chosen as the fundamental units,then what is the dimensional formula for surface tension?

Vedclass Test Series

Exam Paper Generator

Online Exam Module