Physics - NLM Question with Solution | TestHub

Minimum force required to move a body up a rough inclined plane,
${\mathrm{F}}_1=\mathrm{mg}(\sin \mathrm{\theta }+\mathrm{\mu cos}\mathrm{\theta })$

Minimum force required to prevent the body from sliding down the rough inclined plane,
${\mathrm{F}}_2=\mathrm{mg}\left(\sin \mathrm{\theta }-\mathrm{\mu cos}\mathrm{\theta }\right)$

According to the question,
${\mathrm{F}}_1=3{\mathrm{F}}_2$
$\mathrm{mg}\left(\sin \mathrm{\theta }+\mathrm{\mu cos}\mathrm{\theta }\right)=3\left(\mathrm{mgsin}\mathrm{\theta }-\mathrm{\mu mgcos}\mathrm{\theta }\right)$
$4\mathrm{\mu }\cos \mathrm{\theta }=2\sin \mathrm{\theta }$
$\sin \mathrm{\theta }=2\mathrm{\mu }\cos \mathrm{\theta }$
$\tan \mathrm{\theta }=2\mathrm{\mu }=\frac{1}{\sqrt{3}}$
$\mathrm{\theta }=30°$