Water jet coming out of a stationary horizontal tube at speed v strikes horizontally a massive wall moving in opposite direction with same speed. Water comes to rest relative to wall after striking. Treating A as cross-section of jet and density of water as `rho` Select the correct alternative(s)

Options

A. force exerted on the wall is `2rhoAv^(2)`
B. force exerted on the wall is `4rhoAv^(2)`
C. rate of change of kinetic energy of water jet striking the wall is `8rhoAv^(3)`
D. rate of change of kinetic energy of water jet striking the wall is zero.

Answer

B, D

Explanation

mass rate of strike `(dm)/(dt) = A(2v)rho`
Change in velocity during strike `=Deltav=vec(v)_(f)-vec(v)_(i)=(-v)-(v)=-2v`
Thrust force on jet `=Deltav (dm)/(dt)=(dm)/(dt)(-2v)=-4rhoAv^(2)`
Thrust force on wall =-Thrust force on jet `=4rhoAv^(2)`
`(d(KE))/(dt)=1/2 (dm)/(dt) (v_(f)^(2))-1/2(dm)/(dt)(v_(i)^(2))=1/2(dm)/(dt)[(-v)^(2)-v^(2)]=0`