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A block slides down on an incline of angle $30^{\circ}$ with an acceleration $\frac{g}{4}$. Find the kinetic friction coefficient.
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Verified Answer
The correct answer is:
$\frac{1}{2 \sqrt{3}}$
Consider the situation
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
$\begin{aligned} \mu_n & =\frac{F}{N}=\frac{m g}{4 m g \frac{\sqrt{3}}{2}} \\ & =\frac{1}{2 \sqrt{3}}\end{aligned}$
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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