A) \[F\le \mu mg\]
B) \[F=\mu mg\]
C) \[mg<F<mg\sqrt{1+{{\mu }^{2}}}\]
D) \[mg\ge F>mg\sqrt{1-{{\mu }^{2}}}\]
Correct Answer: C
Solution :
If the body is not moving, \[F=f\] Where f is the force of friction of the body, clearly \[O\le F<\mu mg\] or \[O\le F<\mu mg\,(=f)\] Now, the force by the surface on the body. \[F=\sqrt{{{f}^{2}}+{{R}^{2}}}\] \[=\sqrt{{{(\mu mg)}^{2}}+{{(mg)}^{2}}}\] ??.(i) or \[F=mg\,\sqrt{{{\mu }^{2}}+1}\] ??.(ii) From equations (0 and (ii) we concludely \[\therefore \] \[mg\le F\le mg\,\sqrt{1+{{\mu }^{2}}}\]
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