A flat plate moves normally towards a discharging jet of water at the rate of `3 m//s`. The jet discharges the water at the rate of `0.1 m^(3)//s` and at the speed of `18 m8//s`. The force exerted on the plate due to the jet is

Options

A. `1800N`
B. `2100N`
C. `2450N`
D. `1560N`

Answer

C

Explanation

Relative velocity of the water jet with respect to the moving plate `=(18+3)=21m//s`. The mass of water hitting the plate per second `=arho(21)`, where `a` is the cross sectional area of the jet
`F=` force normal to the plate
`=` Rate of change of momentum along the direction of the water jet
`=("Mass")xx("velocity")=[arho(21)]21=441arho`
`:. 441xxrhoxx(0.1/18)`
`=(441xx0.1xx1000)/1.8N=2450N`