A cubic block of mass $m$ is sliding down on an inclined plane at $60^{\circ}$ with an acceleration of…

A cubic block of mass $m$ is sliding down on an inclined plane at $60^{\circ}$ with an acceleration of $\frac{\mathrm{g}}{2}$, the value of coefficient of kinetic friction is
  1. $\sqrt{3}-1$
  2. $\frac{\sqrt{3}}{2}$
  3. $\frac{\sqrt{2}}{3}$
  4. $1-\frac{\sqrt{3}}{2}$

Solution


$\mathrm{mg} \sin 60^{\circ}-\mu \mathrm{mg} \cos 60^{\circ}=\mathrm{ma}$
$g \sin 60-\mu g \cos 60=\frac{g}{2}$
$\frac{\sqrt{3}}{2}-\frac{\mu}{2}=\frac{1}{2}$
$\mu=\sqrt{3}-1$

Asked in: JEE Main 2025 (07 Apr Shift 1)

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