## Equilibrium of Coplanar Forces - Basic 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 light string of length l is fastened to two points A and B at the same level at a distance ‘a’ apart. A ring of weight W can slide on the string, and a horizontal force P is applied to it such that the ring is in equilibrium vertically below B. The tension in the string is equal to
•  aW/l
•  law
•  W(l2 + a2)/2l2
•  2W
Solution
The tension in the string is equal to W(l2 + a2)/2l2

Q2.The resultant of the forces 4, 3, 4 and 3 units acting along the lines AB, BC, CD and DA of a square ABCD of side ‘a’ respectively is
•  A force 5√2 through the centre of the square
•  A couple of moment 7a
•  A null force
•  None of these
Solution
The resultant of the forces 4, 3, 4 and 3 units acting along the lines AB, BC, CD and DA of a square ABCD of side ‘a’ respectively is A couple of moment 7a

Q3.  A body of 6.5 kg is suspended by two strings of lengths 5 and 12 metres attached to two points in the same horizontal line whose distance apart is 13 m. The tension of the strings in kg wt. are
•  3,5
•  2.5,6
•  4,5
•  None of these
Solution
A body of 6.5 kg is suspended by two strings of lengths 5 and 12 metres attached to two points in the same horizontal line whose distance apart is 13 m. The tension of the strings in kg wt. are 2.5, 6

Q4. A body of mass 10 kg is suspended by two strings 7 cm and 24 cm long, their other ends being fastened to the extremities of a rod of length 25 cm. If the rod be so held that the body hangs immediately below its middle point, then the tension of the strings in kg wt. are
•  7/5, 24/5
•  14/5, 48/5
•  3/5, 7/5
•  None of these
Solution
If the rod be so held that the body hangs immediately below its middle point, then the tension of the strings in kg wt. are 14/5, 48/5

Q5.A system of five forces whose directions and non-zero magnitudes can be chosen arbitrarily, will never be in equilibrium if n of the forces are concurrent, where
•  n=2
•  n=3
•  n=4
•  n=5
Solution
A system of five forces whose directions and non-zero magnitudes can be chosen arbitrarily, will never be in equilibrium if n of the forces are concurrent, where n=4

Q6. A uniform rod of weight W and length 2l is resting in a smooth spherical bowl of radius r. The rod is inclined to the horizontal at an angle of
•  0
•  1/4
• 3/4
•  4/5
Solution
The rod is inclined to the horizontal at an angle of 0

Q7.There are three coplanar forces acting on a rigid body. If these are in equilibrium, then they are
•  Parallel
•  Concurrent
•  Concurrent or parallel
•  All of these
Solution
All of these

Q8.There is a system of coplaner forces acting on a rigid body represented in magnitude, direction and sense by the sides of a polygon taken in order, then the system is equivalent to
•  A single non-zero force
•  A zero force
•  A couple, where moment is equal to the area of polygen
•  A couple, where moment is twice the area of polygen
Solution
the system is equivalent to A zero force

Q9.Three coplanar forces each equal to P, act at a point. The middle one makes an angle of with each one of the remaining two forces. If by applying force Q at that point in a direction opposite to that of the middle force, equilibrium is achieved, then
•  P=Q
•  P=2Q
•  2P=Q
•  None of these
Solution
If by applying force Q at that point in a direction opposite to that of the middle force, equilibrium is achieved, then 2P=Q

Q10. A 2m long uniform rod ABC is resting against a smooth vertical wall at the end A and on a smooth peg at a point B. If distance of B from the wall is 0.3m, then
•  AB < 0.3m
•  AB < 1.0m
•  AB > 0.3m
•  AB > 1.0m
Solution
If distance of B from the wall is 0.3m, then AB < 1.0m or AB > 0.3m

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