Sand is being dropped from a stationary dropper at a rate of 0 . 5 kg s - 1 on a conveyor belt moving with a velocity of 5 m s - 1 . The power needed to keep belt moving with the same velocity will be

Step-by-step solution

When the sand is dropped on the conveyor belt its velocity will become equal to that of the conveyor. Therefore, v = 5   m   s - 1 . The force required to keep the conveyor belt moving will be equal to the gain in the momentum by the sand per second. ⇒ F = d m d t v ⇒ F = 0 . 5 × 5 = 2 . 5   N Now the power required to keep the conveyor belt moving will be, P = F v ⇒ P = 2 . 5 × 5 = 12 . 5   W .