question_answer

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?

A)  Zero                                     

B) \[2\text{ }m/{{s}^{2}}\]

C)  \[1.5\text{ }m/{{s}^{2}}\]           

D)  5 m/s

Correct Answer: A

Solution :

                 We can realise the situation as shown. Maximum retadation. \[a=\frac{{{f}_{k}}-mg\sin \theta }{m}\] \[=\frac{{{u}_{k}}mg\cos \theta -mg\sin \theta }{m}\] \[=\frac{\frac{1}{\sqrt{3}}mg\cos {{30}^{o}}-mg\sin {{30}^{o}}}{m}(\theta ={{30}^{o}})\] \[=\frac{\frac{1}{\sqrt{3}}g\times \frac{\sqrt{3}}{2}-g\times \frac{1}{2}}{1}\] \[=0\] Hence, under the effect of kinetic friction between,   block   and   inclined   plane, acceleration of block is zero.