A) \[2\,\,a{{\upsilon }^{2\,\,}}\,p\,\,\cos \,\theta \]
B) \[a{{\upsilon }^{2\,\,}}\,p\,\,\cos \,\theta \]
C) \[2\,\,\,a\upsilon \,\,p\,\,\cos \,\theta \]
D) \[a\upsilon \,\,p\,\,\cos \,\theta \]
Correct Answer: A
Solution :
Normal component of velocity\[=v\cos \theta \] Initial momentum\[=v\cos \theta \] Final momentum\[=mv\cos \theta \] Change in momentum\[=-2mv\cos \theta \] Momentum imparted to wall\[=+2mv\cos \theta \] \[\therefore \] \[m=\rho \times V=\rho \times a\times v\] Force\[=\frac{\Delta p}{\Delta t}=2a{{v}^{2}}\rho \cos \theta \]
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