From the following combinations of physical c | vedclass

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

Question

(B) physical quantity has the same value in different systems of units if it is dimensionless. We check the dimensions of the given expression $\frac{

Vedclass · Accepted Answer

$\frac{e^2}{2\pi \varepsilon _0 G m_e^2}$

Vedclass · Answer

(B) physical quantity has the same value in different systems of units if it is dimensionless. We check the dimensions of the given expression $\frac{e^2}{2\pi \varepsilon _0 G m_e^2}$.The dimensions of the constants are:$e = [M^0 L^0 T^1 A^1]$$\varepsilon _0 = [M^{-1} L^{-3} T^4 A^2]$$G = [M^{-1} L^3 T^{-2}]$$m_e = [M^1 L^0 T^0]$Substituting these into the expression:$\frac{[T^2 A^2]}{[M^{-1} L^{-3} T^4 A^2] [M^{-1} L^3 T^{-2}] [M^2]} = \frac{[T^2 A^2]}{[M^{-1-1+2} L^{-3+3} T^{4-2} A^2]} = \frac{[T^2 A^2]}{[M^0 L^0 T^2 A^2]} = 1$Since the expression is dimensionless,its value remains constant across all systems of units.

From the following combinations of physical constants (expressed through their usual symbols),the only combination that would have the same value in different systems of units is:

Similar Questions

$A$ force $F$ acting on an object is given by $F = a \sqrt{x} - bt$,where $x$ is the distance in meters and $t$ is the time in seconds. The units of $a$ and $b$ are respectively:

In the expression $P = El^2m^{-5}G^{-2}$,$E$,$l$,$m$ and $G$ denote energy,angular momentum,mass and gravitational constant respectively. Show that $P$ is a dimensionless quantity.

$A$ physical quantity $x$ depends on quantities $y$ and $z$ as follows: $x = Ay + B \tan(Cz)$,where $A, B,$ and $C$ are constants. Which of the following do not have the same dimensions?

If the units of force,energy,and velocity are respectively $10\, N$,$100\, J$,and $5\, m/s$,then the units of length,mass,and time will be:

If force $(F)$,velocity $(V)$,and time $(T)$ are taken as fundamental units,then the dimensions of mass are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module