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****Equilibrium of Coplanar Forces - Advance Level**

**Equilibrium of Coplanar Forces - Advance Level**

**Dear Readers,**

Statics is the branch of mechanics that is concerned with the analysis of loads acting on physical systems that do not experience an acceleration, but rather, are in static equilibrium with their environment.
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**Q1.**A uniform rod AB movable about a hinge at A rests with one end in contact with a smooth wall. If be the inclination of the rod to the horizontal, then reaction at the hinge is

Solution

The reaction at the hinge is W/2 (√3 + cosec

The reaction at the hinge is W/2 (√3 + cosec

^{2}α)**Q2.**A uniform rod AB, 17m long whose mass in 120kg rests with one end against a smooth vertical wall and the other end on a smooth horizontal floor, this end being tied by a chord 8m long, to a peg at the bottom of the wall, then the tension of the chord is

Solution

The tension of the chord is 32 kg wt

The tension of the chord is 32 kg wt

**Q3.**Forces of magnitudes 3, P, 5, 10 and Q Newton are respectively acting along the sides AB, BC, CD, AD and the diagonal CA of a rectangle ABCD, where AB= 4 m and BC =3m. If the resultant is a single force along the other diogonal BD then P,Q and the resultant are

Solution

the resultant are 4,10

the resultant are 4,10

^{5}/_{12},12^{11}/_{12}

**Q4.**A uniform rod AB of length a hangs with one end against a smooth vertical wall, being supported by a string of length l, attached to the other end of the rod and to a point of the rod vertically above B. If the rod rests inclined to the wall at an angle θ, then cos

^{2}θ =

Solution

cos

cos

^{2}θ = (l^{2}- a^{2}) / 3a^{2}**Q5.**The resultant of two forces sec B and sec C along sides AB,AC of triangle ABC is a force acting along AD,where D is

Solution

D is Foot of perpendicular from A on BC

D is Foot of perpendicular from A on BC

**Q6.**Three coplanar forces each of weight 10 kilogram are acting at a particle. If their line of actions make same angle, then their resultant force will be

Solution

resultant force will be zero

resultant force will be zero