Physics questions (statics)

1. A heavy uniform sphere of radius a and weight W has a light
inextensible string attached to a point on its surface. The other
end is attached to a rough vertical wall. The sphere rests in equilibrium
touching the wall at a distance h below the point of attachment to the
wall, and is about to slip.
(a) If the coefficient of friction between the sphere and the wall is k, find
the inclination of the string to the vertical.
(b) If k= h/2a, show that the tension in the string is (W(1 + k二次方)1/2次方)/(2k).

2. A uniform rod AB, length 4a, weight W rests at 60 Deg to a smooth
vertical wall. It is supported with the end A in contact with the wall by
an elastic string connecting a point C on the rod to a point D on the
wall vertically above A. If the natural length of the string is 3a/4 and the
distances AC and AD are a,
(a) find the modulus of elasticity of the string in terms of W

3. A uniform rod AB of mass M and length b is smoothly hinged at A
to a vertical wall. It is kept in a horizontal position by a light string
having one end attached to B and the other end to a point C on the
wall at a distance 3b/a vertically above A. A small mass M/2 is attached
to the rod at a point D, where AD=3b/a.
(a) Find the tension in the string and the magnitude and direction of the
reaction on the rod at A.