question_answer

What is the maximum value of the force F such that the block shown in the arrangement does not move?

A)  20 N                                     

B)  10 N

C)  12 N                                     

D)  15 N

Correct Answer: A

Solution :

                                Free body diagram (FBD) of the block (shown by a dot) is shown in figure. For vertical equilibrium of the block \[N=mg+F\sin {{60}^{o}}=\sqrt{3}g+F\times \frac{\sqrt{3}}{2}\]        ...(1) For no motion, force of friction                 \[f\ge F\cos {{60}^{o}}\] Or           \[\mu N\ge F\cos {{60}^{o}}\]    Or           \[\frac{1}{2\sqrt{3}}\left( \sqrt{3}g+F\frac{\sqrt{3}}{2} \right)\ge \frac{F}{2}\] Or           \[g\ge \frac{F}{2}\]or\[F\le 2g\]or\[20\,N\]