NUMERICAL QUESTIONS

                             BASED ON

    RESOLUTION & PARALLELOGRAM LAW OF FORCES

                    ENGINEERING MECHANICS

1.  Two equal vectors have their resultant equal to either of them. At what angle are they inclined to each other?

2.  Two forces 5 N and 10 N inclined at an angle of 30⁰ are acting on a particle. Find the resultant force and its direction.

3.  Two equal forces have a resultant equal to 3/2 times the either force. At what angle they are inclined to each other?

4.  At what angle the two forces (F₁+F₂) and (F₁-F₂) act so that the resultant is √2(F₁²+F₂²).

5.  A horse exerts a force of 320 N at an angle of 30⁰ to the horizontal. Find the force used by the horse in the horizontal direction.

6.  Calculate the resultant of the following forces at a point, making use of resolution process.

1-    100√2 dyne along north-east

2-    980√2 dyne along north-west

3-    1960 dyne along south.

7.   What is the angle between 2 N force and 3 N force so that their resultant is 4 N?

8.  The resultant of two forces of magnitudes 12 N and 3 N on a body is 13.74 N. Find the angle between the two forces. What is the direction of the resultant force w.r.t. 12 N force?

9.  Two forces whose magnitudes are in the ratio of 3:5 give a resultant of 35 N. If the angle of inclination is 60⁰, find the magnitude of each force.

10.                    Resultant of two equal forces acting at right angle to each other is 14.14 N. Find the magnitude of each force.

11.                    At what angle do the forces (P+Q) and (P-Q) act so that the resultant is √(3P²+Q²) ?

12.                    Two forces acting on a particle in opposite directions have a resultant of 10 kgf. If they act at right angle to each other, the resultant is 50 kgf. Find the two forces.

13.                   The resultant f two forces 3P and 2P is R. If the first force is doubled then the resultant is also doubled. Find the angle between the two forces.

14.                   The resultant of two forces P and Q is R. if one of the forces is reversed in direction, then the resultant becomes  S. Prove that, R² +S² = 2.(P²+Q²)

15.                    Two forces when acting at right angles produce a resultant of √10 N and when acting at 60⁰ produce a resultant of √13 N. Find the two forces.