If the velocity of light c , the constant of gravitation G and Planck's constant h be chosen as fund

Question

If the velocity of light c , the constant of gravitation G and Planck's constant h be chosen as fundamental units, the dimension of mass in the new system will be\

Professor PC Thomas Classes · Answer

We start with $F=\frac{G m_{1} m_{2}}{d^{2}}$\ $\mathrm{m}_{1} \mathrm{~m}_{2}=\frac{\mathrm{Fd}^{2}}{\mathrm{G}}$\ $\mathrm{M}^{2}=\frac{(\mathrm{Fd}) \mathrm{d}}{\mathrm{G}}$\ Fd $=$ work and so has the dimension of energy $=\mathrm{h} 
u$ Therefore Fd can be replaced by $\mathrm{h} 
u$\ $M^{2}=\frac{h v d}{G}=\frac{h}{G}(v d)$\ $v \mathrm{~d}=$ frequency $	imes$ length\ It has the dimensions of velocity $	herefore$ vd can be replaced by velocity of light c .\ $\mathrm{M}^{2}=\frac{\mathrm{hc}}{\mathrm{G}} \quad 	herefore \mathrm{M}=$\