Consider three masses m_1, m_2 and m_3 (m_1 | vedclass

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(C) An object begins to slide down an inclined plane when the angle of inclination (also called the angle of repose) is equal to the angle of friction

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$m_1, m_2$ and $m_3$ begin to slide at the same inclination angle.

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(C) An object begins to slide down an inclined plane when the angle of inclination (also called the angle of repose) is equal to the angle of friction. Let $	heta$ be the angle at which a mass begins to slide down an incline.At the verge of sliding,the force of static friction $f_s$ is equal to the downward component of gravity.$f_s = mg \sin 	heta$Since $f_s = \mu N$ and the normal force $N = mg \cos 	heta$,we have:$\mu (mg \cos 	heta) = mg \sin 	heta$$\mu = \frac{\sin 	heta}{\cos 	heta} = 	an 	heta$$	heta = 	an^{-1} \mu$Since the angle of repose $	heta$ depends only on the coefficient of static friction $\mu$ and is independent of the mass $m$ of the body,all three masses will begin to slide at the same instant at the same inclination angle $	heta$.

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