Physics - NLM Question with Solution | TestHub

For upward motion,$F_{up}=mg\left(\sin \theta +\mu \cos \theta \right)$......(i)

For downward motion,$F_{down}=mg\left(\sin \theta -\mu \cos \theta \right)$......(ii)



According to the question,

$F_{up}=2F_{down}$

$mg\left(\sin \theta +\mu \cos \theta \right)=2mg \left(\sin \theta -\mu \cos \theta \right)$

$\sin \theta +\mu \cos \theta =2\sin \theta -2\mu \cos \theta$

$3\mu \cos \theta =\sin \theta$

$\mu =\frac{1}{3}\tan \theta$

$\mu =\frac{1}{3}\times \tan 60°$

$\Rightarrow$$\mu =\frac{1}{3}\sqrt{3}=\frac{1}{\sqrt{3}}$