A block slides down on an inclined surface of inclination $30^o$ with the horizontal. Starting from rest it covers $8\, meter$ in the first two seconds. The coefficient of friction is $(g = 10\, ms^{-2})$
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When the block starts sliding from the top of the incline, then after 2 seconds
${\mathrm{u}=0, \mathrm{t}=2 \mathrm{s}, \mathrm{s}=8 \mathrm{m}, \mathrm{a}=?} $
${\mathrm{S}=\mathrm{ut}+\frac{1}{2} \mathrm{at}^{2}}$
$\text { where } a=\operatorname{gsin} 30^{\circ}-\mu g \cos 30^{\circ} $
$=\frac{g}{2}[1-\sqrt{3} \mu] $
$\text { Thus } 8=0+\frac{1}{2} \frac{g}{2}(1-\sqrt{3} \mu) \times 4$
$ 1-\sqrt{3} \mu =\frac{8}{\mathrm{g}}=\frac{8}{10}=\frac{4}{5} $
$ \sqrt{3} \mu =1-\frac{4}{5}=\frac{1}{5} $
$\mu =\frac{1}{5 \sqrt{3}} $
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