A sand dropper drops sand of mass $m(t)$ on a conveyer belt at a rate proportional to the square roo

Question

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

Professor PC Thomas Classes · Answer

(c) : Power $=$ Force × Velocity $=\vec{F} \cdot \vec{v}$ As, $\quad F=\frac{d p}{d t} \Rightarrow F=\frac{d}{d t}(m \cdot v)$\ $F=\left(\frac{d m}{d t}ight) \cdot v=C(\sqrt{v}) v$ where ' $C$ ' is constant