6 A uniform solid cylinder, L, has base radius 5 cm , height 24 cm and mass 5 kg . L is placed on a rough plane inclined at an angle \(\alpha\) to the horizontal, as shown in Fig. 6.
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\caption{Fig. 6}
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- On the copy of Fig. 6 in the Printed Answer Booklet mark the forces acting on L .
The coefficient of friction between L and the plane is 0.3 . Initially \(\alpha\) is \(15 ^ { \circ }\).
- Show that L rests in equilibrium on the plane.
A couple is applied to L . It is given that L will topple if the couple is applied in an anticlockwise sense, but L will not topple if the couple is applied in a clockwise sense.
- Find the range of possible values of the magnitude of the couple.
The couple is now removed and the plane is slowly tilted so that \(\alpha\) increases.
- Determine whether L topples first without sliding or slides first without toppling.