1.

Sand drops from a stationary hopper at the rate of `5kg//s` on to a conveyor belt moving with a constant speed of `2m//s`. What is the force required to keep the belt moving and what is the power delivered by the motor, moving the belt?

Answer» Correct Answer - A::B
Relative velocity of sand is `2m//s` in backward direction. Since mass is increasing, therefore thrust force is in the direction of relative velocity (backwards).
Thrust force `=v_r(+(dm)/(dt))`
`=(5)(2)=10N` (backwards)
`:.` Force needed `(F_(ext))` to move the belt with constant velocity `(F_(n et)=0)` is
`F_(ext)=F=10N` (in forward direction)
`P=F_(ext) v=20W`


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