A sand dropper drops sand of mass m(t)$m(t)$ on a conveyer belt at a rate proportional to the square root of speed (v$v$) of the belt, i.e. fracdmdt propto sqrtv$\frac{dm}{dt} \propto \sqrt{v}$ . If P$P$ is the power delivered to run the belt at constant speed then which of the following relationship is true?

### Related Formula f_s leq mu_s N$$f_s \leq \mu_s N$$ F_c = mromega^2$$F_c = mr\omega^2$$ ### Core Logic

To prevent the coin from slipping, the static friction must provide the necessary centripetal force for circular motion. f = momega^2 r$f = m\omega^2 r$ The normal force on the flat disc is N = mg$N = mg$. The maximum static friction is f_textmax = mu N = mu mg$f_{\text{max}} = \mu N = \mu mg$. For no slipping: m r omega^2 leq mu mg$$m r \omega^2 \leq \mu mg$$ omega^2 leq fracmu gr$$\omega^2 \leq \frac{\mu g}{r}$$ omega_textmax = sqrtfracmu gr$$\omega_{\text{max}} = \sqrt{\frac{\mu g}{r}}$$ ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Physics: Laws Of Motion