question_answer

A block of mass m is lying on the edge having inclination angle \[{{x}^{2}}+{{y}^{2}}=9,\]Wedge is moving with a constant acceleration, a  \[\left( \frac{3}{2},\frac{1}{2} \right)\] The minimum value of coefficient of friction \[\left( \frac{1}{2},\frac{3}{2} \right)\] so that m remains stationary with respect to wedge is

A) \[\left( \frac{1}{2},\frac{1}{2} \right)\]                                   

B) \[\left( \frac{1}{2},\pm \sqrt{2} \right)\]

C) \[{{y}^{2}}-kx+8=0,\]                                     

D) \[\frac{1}{8}\]

Correct Answer: B

Solution :

FBD of m in frame of wedge \[{{\alpha }_{\max }}\] Now,\[{{\sin }^{-1}}\left[ \frac{{{n}_{1}}}{{{n}_{2}}}\cos \left( {{\sin }^{-1}}\left( \frac{{{n}_{2}}}{{{n}_{1}}} \right) \right) \right]\] \[{{\sin }^{-1}}\left[ {{n}_{1}}\cos \left( {{\sin }^{-1}}\left( \frac{1}{2} \right) \right) \right]\]\[{{\sin }^{-1}}\left( \frac{{{n}_{1}}}{{{n}_{2}}} \right)\] \[{{\sin }^{-1}}\left( \frac{{{n}_{1}}}{{{n}_{1}}} \right)\]\[\frac{dy}{dt}<0.\]