Physics - Circular Motion Question with Solution | TestHub

While the block does not slide, friction balances $$mg\sin \theta$$. At $$\theta =30^{\circ }$$: $$f=mg\sin 30^{\circ }=5\mathrm{N}$$, below $$\mu mg\cos 30^{\circ }\approx 6.5\mathrm{N}$$, so static - (A) true.

At $$\theta =37^{\circ }$$: $$mg\sin 37^{\circ }=6\mathrm{N}=\mu mg\cos 37^{\circ }=\frac{3}{4}\cdot 10\cdot \frac{4}{5}$$, so acceleration is zero (limiting equilibrium) - (B) true.

At $$\theta =45^{\circ }$$: required $$5\sqrt{2}\mathrm{N}$$ exceeds $$\mu mg\cos 45^{\circ }=3.75\sqrt{2}\mathrm{N}$$, so the block slides; friction is not $$5\sqrt{2}\mathrm{N}$$ and $$a=g(\sin 45^{\circ }-\mu \cos 45^{\circ })=1.25\sqrt{2}m/{\mathrm{s}}^2$$ - (C), (D) false.

Answer: (A), (B)