Question

Consider a new system of units in which c (speed of light in vacuum), h (Planck's constant) and G (gravitational constant) are taken as fundamental units. Which of the following would represent mass in this new system ?

• A. $\sqrt{\frac{hC}{G}}$
• B. $\sqrt{\frac{GC}{h}}$
• C. $\sqrt{\frac{hG}{c}}$
• D. $\sqrt{hGC}$

Answer 1

Answer: (A)

$\sqrt{\frac{hC}{G}}$

Answer 2

[h] = ML²T^–1, [C] = LT^–1, [G] = M^–1L³T^–2

(1) $\sqrt{\frac{hc}{G}}$ = $\sqrt{ML^{2}T^{- 1}.\frac{LT^{- 1}}{M^{- 1}L^{3}T^{- 2}}}$

= $\sqrt{M^{2}}$ = m