Parallel Forces, Moment and Couples- Advance Level

Parallel Forces, Moment and Couples- 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. .

Q1. Forces P, 3P, 2P and 5P act along the sides AB, BC, CD and DA of the square ABCD. If the resultant meets AD produced at the point E, then AD : DE is

•  1 : 2
•  1 : 3
•  1 : 4
•  1 : 5

Solution
AD : DE is 1 : 4

Q2.A horizontal rod AB is suspended at its ends by two vertical strings. The rod is of length 0.6m and weighs 3 Newton. Its centre of gravity G is at a distance 0.4m from A. Then the tension of the string at A is

•  0.2 N
•  1.4 N
•  0.8 N
•  1 N

Solution
the tension of the string at A is 1 N

Q3.  A horizontal rod of length 5m and weight 4 N is suspended at the ends by two strings. The weights of 8N, 12N, 16N and 20N are placed on the rod at distance 1m, 2m, 3m and 4 m from one end of the rod. The tension in the strings are

•  26N,34N
•  20N,30N
•  10N,40N
•  None of these

Solution
The tension in the strings are 26N,34N

Q4. Two unlike parallel forces P and Q act at points 5m apart. If the resultant force is 9N and acts at a distance of 10m from the greater force P, then

•  P=16N,Q=7N
•  P=15N,Q=6N
•  P=27N,Q=18N
•  P=18N,Q=9N

Solution
If the resultant force is 9N and acts at a distance of 10m from the greater force P, then P=27N,Q=18N

Q5.A force √5 units act along the line (x-3)/2=(y-4)/(-1), the moment of the force about the point (4,1) along z-axis is

•  0
•  5√5
•  -√5
•  5

Solution
 the moment of the force about the point (4,1) along z-axis is 5

Q6. The height from the base of a pillar must be end B of a rope AB of given length be fixed so that a man standing on the ground and pulling at its other end with a given force may have the greatest tendency to make the pillar overturn is

•  AB
•  AB/2
• AB/√2
•  None of these

Solution
The height from the base of a pillar must be end B of a rope AB of given length be fixed so that a man standing on the ground and pulling at its other end with a given force may have the greatest tendency to make the pillar overturn is AB/√2

Q7.n a triangle ABC right angled at C, the lengths of sides AC and BC are 3 cm and 4 cm respectively. Parallel forces each equal to P act at the vertices A,B,C and parallel forces each equal to 2P act at the middle points of all the sides of the triangle. The distance of C.G. from the vertex C is

•  2/3 cm
•  4/3 cm
•  5/3 cm
•  None of these

Solution
The distance of C.G. from the vertex C is 5/3 cm

Q8.A uniform rod BC of length 6 cm and weight 2 kg can turn freely about the fixed point B. The rod is attached to the point A by a string AC of length 8 cm. The points A and B are in a horizontal line at a distance 10 cm. The tension in the string is

•  3/5 kg wt
•  1/5 kg wt
•  2/5 kg wt
•  None of these

Solution
The tension in the string is 3/5 kg wt

Q9.If each of the two unlike parallel forces P and Q (P>Q) acting at a distance d apart be increased by S, then the point of application of the resultant is moved through a distance

•  d/(P-Q)
•  S/(P-Q)
•  Sd/(P-Q)
•  S/d(P-Q)

Solution
the point of application of the resultant is moved through a distance Sd/(P-Q)

Q10. Three forces P, Q and R act along the sides BC, AC and BA of an equilateral triangle ABC. If their resultant is a force parallel to BC through the centroid of the triangle ABC, then

•  P=Q=R
•  P=2Q=2R
•  2P=Q+2R
•  2P=2Q=R

Solution
If their resultant is a force parallel to BC through the centroid of the triangle ABC, then P=2Q=2R