A) \[gh\rho a\]
B) \[\frac{2gh}{\rho \,a}\]
C) \[2\rho agh\]
D) \[\frac{\rho gh}{a}\]
Correct Answer: C
Solution :
Net force (reaction) = \[F={{F}_{B}}-{{F}_{A}}\]\[=\frac{d{{p}_{B}}}{dt}-\frac{d{{p}_{A}}}{dt}\] \[=a{{v}_{B}}\rho \times {{v}_{B}}-a{{v}_{A}}\rho \times {{v}_{A}}\] \ \[F=a\rho \left( v_{B}^{2}-v_{A}^{2} \right)\] ?(i) According to Bernoulli's theorem \[{{p}_{A}}+\frac{1}{2}\rho v_{A}^{2}+\rho gh={{p}_{B}}+\frac{1}{2}\rho v_{B}^{2}+0\] Þ \[\frac{1}{2}\rho \left( v_{B}^{2}-v_{A}^{2} \right)=\rho gh\]Þ \[v_{B}^{2}-v_{A}^{2}=2gh\] From equation (i), \[F=2a\rho gh.\]You need to login to perform this action.
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