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  • A block of mass m slides down the plane inclined at angle 30 with an acceleration . The val

A block of mass m slides down the plane inclined at angle 30 with an acceleration \frac{g}{4}. The value of coefficient of kinetic friction will be:

Option: 1

\frac{1}{2\sqrt{3}}


Option: 2

\frac{\sqrt{2}}{3}


Option: 3

\frac{2\sqrt{3}+1}{2}


Option: 4

\frac{2\sqrt{3}-1}{2}


Answers (1)

best_answer

\begin{aligned} & \mathrm{f}_{\mathrm{k}}=\mu \mathrm{N} \\ & \mathrm{N}=\mathrm{mg} \cos \theta \\ & \mathrm{f}_{\mathrm{k}}=\mu \mathrm{mg} \cos \theta \\ & \mathrm{a}=\frac{\mathrm{mg} \sin \theta-\mu \mathrm{mg} \cos \theta}{\mathrm{m}} \\ & \mathrm{a}=\mathrm{g} \sin 30^{\circ}-\mu \mathrm{g} \cos 30^{\circ} \\ & \frac{\mathrm{g}}{4}=\mathrm{g}\left[\frac{1}{2}-\frac{\sqrt{3} \mu}{2}\right] \\ & \frac{1}{2}=1-\sqrt{3} \mu \\ & \sqrt{3} \mu=\frac{1}{2} \end{aligned}

\mu=\frac{1}{2\sqrt{3}}

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SANGALDEEP SINGH

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