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A **uniform cube** of side $a$ sits on a rough incline. As $\theta$ is increased, the cube **topples** before sliding if:
A$\mu < 1/2$
B$\mu > 1$ — toppling at $\theta = 45°$ requires $\mu > 1$
C$\mu = 1/2$
DCube cannot topple on incline
Answer & Solution
Correct answer: B. $\mu > 1$ — toppling at $\theta = 45°$ requires $\mu > 1$
Toppling when CG line crosses the lower edge: $\tan\theta_{\text{topple}} = (a/2)/(a/2) = 1$, so $\theta_{\text{topple}} = 45°$. Sliding when $\tan\theta > \mu$, so $\theta_{\text{slide}} = \arctan \mu$. For toppling first: $\theta_{\text{topple}} < \theta_{\text{slide}}$ ⇒ $1 < \mu$. So a cube on a low-friction surface slides first; only if $\mu > 1$ does it topple before sliding.
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