Question

In the figure, a horizontal force F is applied such that the block remains stationary. Which of the following statements is false?

• (A) f = mg [where f is the friction force]
• (B) F = N [where N is the normal force]
• (C) F will not produce torque
• (D) N will not produce torque

Answer 1

The Correct Option is D

Explanation:
As the block remains stationary, so for translatory equilibrium,

$\mathrm{\Sigma }{F}_x=0\therefore F=N$and $\sum F_y=0\therefore f=mg$For rotational equilibrium, $\mathrm{\Sigma }t=0$ By taking the torque of different forces about point $\mathrm{O}$ $\overline{t_F}+\overline{{\mathrm{t}}_f}+\overrightarrow{{\mathrm{t}}_N}+\overline{{\mathrm{t}}_{\mathrm{mg}}}=0$As $\mathrm{F}$ and $\mathrm{mg}$ pass through point $\mathrm{O}$ $\therefore \overline{c_f}+\overline{{\tau }_N}=0$As $\overline{{\tau }_f}\ne 0\therefore \overline{{\tau }_N}\ast 0,$ so torques by friction and normal reaction will be in oppositedirections.