question_answer

A coin is placed at the edge of a horizontal disc rotating about a vertical axis through its axis with a uniform angular speed 2 rad \[{{s}^{-1}}\]. The radius of the disc is 50 cm. Find the minimum coefficient of friction between disc and coin so that the coin does not slip \[(g=10m{{s}^{-2}})\].

A) 0.1                  

B) 0.2     

C) 0.3                  

D) 0.4

Correct Answer: B

Solution :

[b] \[{{f}_{1}}=\mu \,mg,\]friction will provide the necessary centripetal force \[f=m{{\omega }^{2}}r\] \[f\le {{f}_{1}}\Rightarrow m{{\omega }^{2}}r\le \mu mg\] \[\Rightarrow \mu \ge \frac{{{\omega }^{2}}r}{g}=\frac{{{2}^{2}}\times 50/100}{10}\] \[\Rightarrow \mu \ge 0.2\]