If the angular momentum of particles of mass m rotating along a circular path of radius r with unifo

Question

If the angular momentum of particles of mass m rotating along a circular path of radius r with uniform speed is L , the centripetal force acting on the particle is\

Professor PC Thomas Classes · Answer

Let the particle of mass m moves with uniform speed v along the circular path of radius r .\ $	herefore$ Angular momentum of the particle, $\mathrm{L}=\mathrm{mvr}$\ Or $\mathrm{v}=\frac{\mathrm{L}}{\mathrm{mr}}$\ Centripetal force acting on the particle is\ $\mathrm{F}=\frac{\mathrm{mv}^{2}}{\mathrm{r}}=\frac{\mathrm{m}\left(\frac{\mathrm{L}}{\mathrm{mr}}ight)^{2}}{\mathrm{r}} \quad$ (using (i)) Note : You can also check it dimensionally, only option ((a) has the dimensions of force\