Applied Mechanics and Graphic Statics
A cylinder will slip on an inclined plane of inclination 0 if the coefficient of static friction between plane and cylinder is

less than (1/3) sin 6
less than (1/3) tan 0
less than (2/3) sin 6
less than (2/3) tan 0

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Applied Mechanics and Graphic Statics
The following statement is one of the laws of Dynamic friction

The magnitude of the kinetic friction bears a constant ratio to the normal reaction between two surfaces. The ratio being slightly less than that in the case of limiting friction
All of these
The force of friction always acts in a direction opposite to that in which a body is moving
For moderate speeds the force of friction remains constant but decreases slightly with the increase of speed

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Applied Mechanics and Graphic Statics
A body of weight ‘w’ placed on an inclined plane is acted upon by a force ‘P’ parallel to the plane which causes the body just to move up the plane. If the angle of inclination of the plane is ‘θ’ and angle of friction is ‘φ’, the minimum value of ‘P’, is

w sin (θ - φ)/cos φ
w sin (φ - θ)/cos φ
w sinθ cos(θ - φ)/sin φ
w cos (θ + φ)/cos φ

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