1.A thin uniform wire AB is bent into the form of a semicircle.Find the inclination of AB to the vertical when the wire is freely suspended from A. A particle equal to the weight of the wire is now attached to B, find the new inclination of AB to the vertical.
2.An uniform lamina is in the form of a square ABCD of side 2 m,E is a point on AD such that ED=xm and the portion EDC is removed. Show that if the lamina is places in a vertical plane with AE on a rough horizontal surface it will topple if
x>3- 根3.If x=1.5 and the weight of the lamina is W, find the least force which must be applied to the lamina to stop it toppling.
3.A particle rests on a rough plane inclined at an angle x to the horizontal. The coefficient of friction between the particle and the plane is y.When the weight of the particle is W, a horizontal force of magnitude P just prevents the particle from slipping down the plane. If however a force of magnitude 2P acts parallel to the plane, the particle is on the point of slipping up the plane. The same force acting on a particle of weight 2W just prevents if from slipping down the same plane. find the values of x and y,and express P in terms of W.