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…

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. \(\frac{dm}{dt}\propto \sqrt{v}\). If P is the power delivered to run the belt at constant speed then which of the following relationship is true?

[JEE Main 2025, 29 Jan (Shift 2)]