Question

Planck's constant h, speed of light c and gravitational constant G are used to form a unit of length L and a unit of mass M. Then the correct option(s) is(are)

• A. $M\propto \sqrt{c}$
• B. $M\propto \sqrt{G}$
• C. $L\propto \sqrt{h}$
• D. $L\propto \sqrt{G}$

Answer 1

Answer: (A), (C), (D)

$E=\frac{hc}{\lambda }$
$E=\frac{-G{m}_1{m}_2}{r}$
$\frac{hc}{\lambda }=\frac{G{m}^2}{r}$
unit of $\lambda$ and r is L
So $M={\left(\frac{hc}{G}\right)}^{1/2}\dots \left(1\right)$
$M\propto \sqrt{c}M\propto \frac{1}{\sqrt{G}}Ans.\left(A\right)$
$E=m{c}^2$
$E=\frac{hc}{\lambda }$
$\frac{hc}{\lambda }=m{c}^2$
$\lambda =\frac{h}{m}$
$\therefore L=\frac{h}{M}$
$L=\frac{h}{{\left(hc\right)}^{1/2}}{G}^{1/2}$ from $\left(1\right)$
$\therefore L\propto \sqrt{G}L\propto \sqrt{h}$