JEE Main202529 Jan 2025Evening ShiftPhysicsWork, Power and EnergyActual
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. dm dt v . If P is the power delivered to run the belt at constant speed then which of the following relationship is true?
Options
- AP v
- BP v
- CP ^2 v^5
- DP ^2 v^3
Correct answer
C. P ^2 v^5
Step-by-step solution
Power = F V and F= d p d t = Rate of change of linear momentum F=V d m d t =K₁ V^ 3 2 , K is constant Power (P)= (K V^ 3 2 ) (V)=K V^ 5 2 So, P^2 V^5