Question

S.I. unit and C.G.S unit of a quantity vary by ${10}^3$ times. It is :

• A. Boltzmann constant
• B. Gravitational constant
• C. Plank's constant
• D. Angular Momentum

Answer 1

The correct option is B Gravitational constant

Boltzmann constant expressed as $J/K$ are expressed as $erg/K$ in CGS unit. The variation is of ${10}^5$.

$Gravitationalconstant=M^{-1}{T}^{-2}{L}^3$

$\left(CGS\right)=\underset{(kg.gm)}{\frac{1}{{10}^3}}\times 1\times -\underset{unit.cm}{{10}^3}={10}^3$
Plank's constant $=M^1{L}^1{T}^{-1}={10}^3\times {10}^2\times 1={10}^5$
Angular Momentum $=M{L}^2{T}^{-1}={10}^3\times ({10}^2{)}^2\times 1={10}^7$