Question

A horizontal force F is applied to a small object P of mass m on a smooth plane inclined to the horizon at an angle θ. If F is just enough to keep P in equilibrium, then F =

• A. $mg\cos^{2}\theta$
• B. $mg\sin^{2}\theta$
• C. $mg\cos\theta$
• D. $mg\tan\theta$

Answer 1

Answer: (D)

$mg\tan\theta$

Answer 2

By applying Lami's theorem at P, we have

$\frac{R}{\sin 90{^\circ}} = \frac{F}{\sin(180{^\circ} - \theta)} = \frac{mg}{\sin(90{^\circ} + \theta)}$

$\Rightarrow \frac{R}{1} = \frac{F}{\sin\theta} = \frac{mg}{\cos\theta} \Rightarrow F = mg\tan\theta$