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:

Find the coefficient of kinetic friction for a block sliding down a $$30°$$ incline with acceleration $$\frac{g}{4}$$.

$$ma = mg\sin 30° - \mu_k mg\cos 30°$$

$$\frac{g}{4} = g\sin 30° - \mu_k g\cos 30°$$

$$\frac{1}{4} = \frac{1}{2} - \mu_k \cdot \frac{\sqrt{3}}{2}$$

$$\mu_k \cdot \frac{\sqrt{3}}{2} = \frac{1}{2} - \frac{1}{4} = \frac{1}{4}$$

$$\mu_k = \frac{1}{4} \cdot \frac{2}{\sqrt{3}} = \frac{1}{2\sqrt{3}}$$

The correct answer is Option B: $$\frac{1}{2\sqrt{3}}$$.