A box of mass 8 kg is placed on a rough inclined plane of...

A box of mass 8 kg is placed on a rough inclined plane of inclination

30^{\circ}

. Its downward motion can be prevented by applying a horizontal force F , then value of F for which friction between the block and the incline surface is minimum, is A box of mass 8 kg is placed on a rough inclined plane of inclination 30^ . Its downward motion can be prevented by

A box of mass 8 kg is placed on a rough inclined plane of inclination 30^ . Its downward motion can be prevented by

Options

A $\frac{80}{\sqrt{3}}$
B $40 \sqrt{3}$
C $\frac{40}{\sqrt{3}}$
D $80 \sqrt{3}$

Correct answer

A. $\frac{80}{\sqrt{3}}$

Step-by-step solution

For friction to be minimum, A box of mass 8 kg is placed on a rough inclined plane of inclination 30^ . Its downward motion can be prevented by

\begin{aligned} \mathrm{F} \cos \theta & =\mathrm{mg} \sin \theta \\ \mathrm{F} & =\mathrm{mg} \tan \theta \\ & =\frac{80}{\sqrt{3}}\end{aligned}

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