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(D) Given: Rate of mass flow $\frac{dm}{dt} = 0.5 \, kg s^{-1}$,Velocity of belt $v = 5 \, m s^{-1}$.When sand falls on the belt,the belt must exert a

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$12.5$

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(D) Given: Rate of mass flow $\frac{dm}{dt} = 0.5 \, kg s^{-1}$,Velocity of belt $v = 5 \, m s^{-1}$.When sand falls on the belt,the belt must exert a force to accelerate the sand to the velocity of the belt.The force required to maintain the constant velocity is equal to the thrust force: $F = \frac{dm}{dt} 	imes v$.$F = 0.5 \, kg s^{-1} 	imes 5 \, m s^{-1} = 2.5 \, N$.The power required to keep the belt moving at a constant velocity is $P = F 	imes v$.$P = 2.5 \, N 	imes 5 \, m s^{-1} = 12.5 \, W$.

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 the belt moving with the same velocity will be: (in $, W$)

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