Question

A horizontal force F is applied such that the block remains stationary then which of the following statement is flase:

• A. f = mg [where f is the friction force]
• B. F = N [where N is the mormal force]
• C. F will not produced torque
• D. N will not produce torque.

Answer 1

Answer: (D)

N will not produce torque.

Answer 2

As the block remains stationary therefore

For translator equilibrium

SF_x = 0$\therefore$ F = N and SF_y = O $\therefore$ f = mg

For rotational equilibrium S$\tau = 0$

By taking the torque of different forces about point O $\overset{\rightarrow}{\tau_{F}} + \overset{\rightarrow}{\tau_{f}} + \overset{\rightarrow}{\tau_{N}} + \overset{\rightarrow}{\tau_{mg}} = 0$

As F and mg passing through point O

$\Rightarrow \mspace{6mu}\mspace{6mu}\overset{\rightarrow}{\tau_{f}} + \overset{\rightarrow}{\tau_{N}} = 0$

As $\overset{\rightarrow}{\tau_{f}} \neq 0$, $\overset{\rightarrow}{\tau_{N}} \neq 0$ and torque by friction and normal reaction will be in opposite direction.