question_answer

A cylinder of height h is placed on an inclined plane, the angle of inclination of which is slowly increased. It begins to slip when the angle of inclination is \[45{}^\circ \]. What is the radius of the cylinder?

A)  h                                

B)  \[\frac{3}{4}h\]

C)  \[\frac{1}{2}h\]                                 

D)  \[\frac{1}{4}h\]

Correct Answer: C

Solution :

 The cylinder will just begin to slip and will not topple, if moment of force \[\Rightarrow \] about A = Moment of N about A \[\lambda =20,\,\frac{20}{3},\,\frac{20}{5},\,\frac{20}{7},...\] \[\phi \] As \[\tan \,\phi =\frac{V}{H}\] hence, \[\theta \] i.e., Vertical line through centre of gravity makes angle \[H'=H\,\cos \,\theta ,\] with the normal to plane.