Physics - NLM Question with Solution | TestHub

For the minimum value of acceleration, friction acts in an upward direction.

$$\begin{array}{rl}& N=ma\sin \theta +mg\cos \theta \\ & mg\sin \theta =f_r+ma\cos \theta \\ & mg\sin \theta =\mu [ma\sin \theta +mg\cos \theta ]+ma\cos \theta \\ & mg\sin \theta -\mu mg\cos \theta =ma\cos \theta +\mu ma\sin \theta \\ & mg(\sin \theta -\mu \cos \theta )=ma(\cos \theta +\mu \sin \theta )\\ & a=\frac{g(\sin \theta -\mu \cos \theta )}{\cos \theta +\mu \sin \theta }\\ & Dividingnumeratoranddenominatorby\cos \theta :\\ & a=\frac{g[\tan \theta -\mu ]}{\mu \tan \theta +1}\end{array}$$