## Equilibrium of Coplanar Forces - Advance Level

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. .

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
•  W/2 (√3 + cosec 2α)
•  W/2(√3+sin 2α)
•  W/2(√3+tan 2α)
•  None of these
Solution
The reaction at the hinge is W/2 (√3 + cosec 2α)

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
•  32 kg wt
•  16 kg wt
•  64 kg wt
•  8 kg wt
Solution
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
•  4,10 5/12,12 11/12
•  5,6,7
•  8,9,10
•  None of these
Solution
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 =
•  (l2 - a2) / a2
•  (l2 - a2) / 2a2
•  (l2 - a2) / 3a2
•  (l2 + a2) / 3a2
Solution
cos 2 θ = (l2 - a2) / 3a2

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
•  Middle point of BC
•  Foot of perpendicular from A on BC
•  D divides BC in the ratio cos B: cos C
•  D divides BC in the ratio cos C: cos B
Solution
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
•  Zero
•  5√2
• 10√2
•  20
Solution
resultant force will be zero

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