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: (D)

$L \propto \sqrt{G}$

Answer 2

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