Q. An ice cube is kept on an inclined plane of angle $ 30{}^\circ $ . Coefficient of kinetic friction between block and incline plane is $ \frac{1}{\sqrt{3}}. $ . What is acceleration of block?
BHUBHU 2006
Solution:
We can realise the situation as shown. Maximum retadation.
$ a=\frac{{{f}_{k}}-mg\sin \theta }{m} $
$=\frac{{{\mu}_{k}}mg\cos \theta -mg\sin \theta }{m} $
$=\frac{\frac{1}{\sqrt{3}}mg\cos {{30}^{o}}-mg\sin {{30}^{o}}}{m}(\theta ={{30}^{o}}) $
$=\frac{\frac{1}{\sqrt{3}}g\times \frac{\sqrt{3}}{2}-g\times \frac{1}{2}}{1} $
$=0 $
Hence, under the effect of kinetic friction between, block and inclined plane, acceleration of block is zero.
