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

JEE Main · 2023 · 29 Jan 2023 · Shift 1 · Laws of Motion

A block of mass

m

slides down the plane inclined at angle

3 0^{\circ}

with an acceleration

\frac{g}{4}

. The value of coefficient of kinetic friction will be :

(A) $\frac{2 3 + 1}{2}$
(B) $\frac{1}{2 3}$ ✓ Correct
(C) $\frac{3}{2}$
(D) $\frac{2 3 - 1}{2}$

Answer: (B)

Solution

Along the incline the equation of motion is

m g sin 3 0^{\circ} - μ m g cos 3 0^{\circ} = ma

with

a = \frac{g}{4}

. Dividing by

m g

gives

\frac{1}{2} - μ \frac{3}{2} = \frac{1}{4}

, so

μ \frac{3}{2} = \frac{1}{4}

. The coefficient of kinetic friction is

\frac{1}{2 3}

JEE Main · 2023 · 29 Jan 2023 · Shift 1 · Single correct option

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