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1.Units, Dimensions and Measurement
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If $\varepsilon_0$ is permittivity of free space, $e$ is charge of proton, $G$ is universal gravitational constant and $m_p$ is mass of a proton then the dimensional formula for $\frac{e^2}{4 \pi \varepsilon_0 G m_p{ }^2}$ is
A
$\left[ M ^1 L ^1 T ^{-3} A ^{-1}\right]$
B
$\left[ M ^0 L ^0 T ^0 A ^0\right]$
C
$\left[ M ^1 L ^3 T ^{-3} A ^{-1}\right]$
D
$\left[ M ^{-1} L ^{-3} T ^4 A ^2\right]$
Solution
(b)
Gravitational force $F_1=\frac{G M_P^2}{r^2}$
Electrostatic force $F_2=\frac{1}{4 \pi \varepsilon_0} \frac{e^2}{r^2}$
$\frac{F_2}{F_1}=\frac{e^2}{4 \pi \varepsilon_0 G M_\rho^2}$
$\therefore$ Dimension less $\left[ M ^{\circ} L ^{\circ} T ^{\circ} A ^{\circ}\right]$
Standard 11
Physics
