A block slides down on an incline of angle 30^ with an acceleration...

A block slides down on an incline of angle

30^{\circ}

with an acceleration

\frac{g}{4}

. Find the kinetic friction coefficient. A block slides down on an incline of angle 30^ with an acceleration (g)/(4) . Find the kinetic friction coefficient.

A block slides down on an incline of angle 30^ with an acceleration (g)/(4) . Find the kinetic friction coefficient.

Options

A $\frac{1}{2 \sqrt{2}}$
B0.6
C $\frac{1}{2 \sqrt{3}}$
D $\frac{1}{\sqrt{2}}$

Correct answer

C. $\frac{1}{2 \sqrt{3}}$

Step-by-step solution

Consider the situation A block slides down on an incline of angle 30^ with an acceleration (g)/(4) . Find the kinetic friction coefficient.

Let the mass of block be

m

. The equation of forces

\begin{aligned} m g \sin 30^{\circ}-f & =\frac{m g}{4} \\ f & =\frac{m g}{4}\end{aligned}

Also,

N=m g \cos 30^{\circ}=m g \frac{\sqrt{3}}{2}

As the block is slipping on the incline, friction is

\begin{aligned} \mu_n & =\frac{F}{N}=\frac{m g}{4 m g \frac{\sqrt{3}}{2}} \\ & =\frac{1}{2 \sqrt{3}}\end{aligned}

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