A) \[\frac{mg}{\rho S{{(V-u)}^{2}}}\]
B) \[\frac{mg}{\rho S{{(2V-u)}^{2}}}\]
C) \[\frac{mg}{\rho S{{(V+u)}^{2}}}\]
D) \[\frac{mg}{\rho S{{(2V+u)}^{2}}}\]
Correct Answer: C
Solution :
[c] Volume of air striking the paper in unit time \[=S(V+u)\] Mass of air striking the paper in unit time \[=\rho S(V+u)\] In reference frame of man, the air molecules strike at a speed \[(V+u)\] and comes to rest. \[\therefore \] Rate of change of momentum for air particles \[=\rho S(V+u)\,\,(V+u)\] \[\therefore \] Force on paper due to air \[=\rho S{{(V+u)}^{2}}\] For the paper to not fall, friction on it must balance its weight. \[{{f}_{\max }}\ge mg\] \[\mu \rho S\,\,{{(V+u)}^{2}}\ge mg\] \[\mu \ge \frac{mg}{\rho S{{(V+u)}^{2}}}\]You need to login to perform this action.
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