The minimum force required to move a body up | vedclass

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(C) The minimum force required to move a body up a rough inclined plane is given by $F_1 = mg(\sin 	heta + \mu \cos 	heta)$.The minimum force requir

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$30$

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(C) The minimum force required to move a body up a rough inclined plane is given by $F_1 = mg(\sin 	heta + \mu \cos 	heta)$.The minimum force required to prevent the body from sliding down the rough inclined plane is given by $F_2 = mg(\sin 	heta - \mu \cos 	heta)$.According to the problem, $F_1 = 3F_2$.Substituting the expressions, we get $mg(\sin 	heta + \mu \cos 	heta) = 3mg(\sin 	heta - \mu \cos 	heta)$.Dividing both sides by $mg$, we have $\sin 	heta + \mu \cos 	heta = 3\sin 	heta - 3\mu \cos 	heta$.Rearranging the terms, $4\mu \cos 	heta = 2\sin 	heta$, which simplifies to $	an 	heta = 2\mu$.Given $\mu = \frac{1}{2\sqrt{3}}$, we have $	an 	heta = 2 	imes \frac{1}{2\sqrt{3}} = \frac{1}{\sqrt{3}}$.Therefore, $	heta = 	an^{-1}(\frac{1}{\sqrt{3}}) = 30^{\circ}$.

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