Mechanical Engineering >> Forces & Force system >> Resultant MCQ >> 1-15

 1. Find the magnitude of two unlike parallel forces P & Q acting at a distance 2m apart. Which is equivalent to a force of 600 N acting at a distance of 600 mm?

(a) 600 N (b) 360 N (c) 300 N (d) 1 N

Ans.: (b) Explanation : P = Q = P \ P ´ 1 = 600 ´ 0.6 = 360 N P = 360 N

2. Four forces P = 150 N (East), Q = 200 N (North), R = 200 N (South) and S = 150 N (West) are acting on member, their resultant is ______.

(a) 0 N (b) 500 N (c) 400 N (d) 300 N

Ans.: (a) Explanation : åFx = 150 – 150=0 åFy = 200 – 200=0 R = (åFx)2 + (åFy)2 = 0 Engineering Mechanics 1.6 Forces and Force System (MCQs) Gigatech Publishing House Igniting Minds

3. The centre of gravity of an isosceles triangle with base a and sides b is ____ from its base.

(a) 4b2 - a2 6 (b) 4a2 - b2 6 (c) 4b2+a2 6 (d) 4a2+b2 6

Ans.: (a) Explanation : In DPQR = 90° b2 = è æ ø ö a 2 2 + h2 b 2 = a 2 4 + h2 h2 = b2 - a 2 4 h2 = 4b2 - a2 4 h = 4b2 - a2 2 C.G. from bottom h/3 C.G. = 4b2 - a2 2 ´ 3 = 4b2 - a2 6

4. Forces of magnitudes 1 N, 2 N, 3 N and 4 N are acting along sides AB, CB, DC and DA of a rectangle respectively. The magnitude of resultant is

(a) 7.21 N (b) 4 N (c) 6 N (d) 0N

Ans.: (a) Explanation: SFx = 1 + 3 = 4 N R = 4 2+ (–62 ) R = 7.21 N \ SFy = – 2 – 4 = – 6 N 

5. If forces of 1N, 2 N, 3 N, 4 N, 5 N and 6 N act at in order along the sides of regular hexagon, then the resultant is _____.

(a) 0 (b) 6 N (c) 12 N (d) 18 N

Ans.: (b) Explanation : Interior angles = (2n – 4) 90 = (2 ´ 6 – 4) ´ 90 = 720 Each angle = 720 6 = 120° åFx = 1 + 2 cos 60° – 3 cos 60° – 4 – 5 cos 60° + 6 cos 60° = – 3 N åFy = 2 sin 60° + 3 sin 60° – 5 sin 60° – 6 sin 60° = – 5.19 N Resultant (R) = åFx2 + åFy2 = (-3)2 + (-5.19)2 = 6 N

6. Three forces 7 N, 14 N and 28 N act along three sides of an equilateral triangle AB, BC and CA. Side AB being horizontal. The resultant of system is

(a) 18.15 N (b) 31.77 N (c) 23.71 N (d) 71.31 N

Ans.: (a) Engineering Mechanics 1.7 Forces and Force System (MCQs) Gigatech Publishing House Igniting Minds Explanation : SFx = 7 – 14 cos 60 – 28 cos 60° = – 14 N SFy = 14 sin 60° – 28 sin 60 = – 12.12 N R = (– 14)2+ (– 12.12)2 = 18.51

7. The resultant of two perpendicular forces of magnitude F each will be

(a) 2 P (b) 2P (c) 2 P (d) P

Ans.: (a) Explanation : R2 = f2 1+f2 2+2f1f2cosq f1 = f2= f And q = 90° R2 = f2+f2 1+2f×f×cos90° R2 = f2 1+f2 R2 = 2f2 R = 2 × f = 2 P

8. Two forces act an angle of 130°. If the greater force is 60 N and their resultant is perpendicular to the smaller force, the smaller force is _______.

(a) 0 N (b) 38.57N (c) 300 N (d) 25 N.

Ans.: (b) Explanation : åFx = P ‒ 60 cos 50°= 0 = 38.57 N \ Smaller force = 38.57 N R = is along 90° \ åFy = 0 

9. Forces 10 N, 20 N, 30 N and 40 N act along sides of a rectangle. Their resultant force will be ______.

(a) 28.28 N (b) 40 N (c) 100 N (d) 32.32 N

Ans.: (a) Explanation : åFx = 10 – 30 = – 20 åFy = 20 – 40 = – 20 R = (20)2 + (20)2 R = 28.28 N

10. Two parallel forces P1 and P2 act on rigid body at points A and B lying on a straight line such that AB = 6 m. Resultant of these two forces at a point C lying on AB such that AB = 2 : 3_______.

(a) like parallel forces (b) unlike parallel forces (c) both (a) and (b) (d) perpendicular forces

Ans.: (a) Explanation : \ Both force P1 and P2 vertical so Resultant also vertical Engineering Mechanics 1.8 Forces and Force System (MCQs) Gigatech Publishing House Igniting Minds

11. Four forces 10N, 20N, 30N and 40N (all tensile) act at a point at angles of 25°, 50°, 75° and 100° clockwise from +ve X-axis. The sum of components of all forces along axis parallel to X-axis is

(a) 36.64N (b) 87.91N (c) -36.64N (d) -87.91N

Ans.: (a) Explanation : åFx = 10 cos25° + 20 cos50° + 30 cos75° + 40 cos80° = 9.07 + 12.86 + 7.76 + 6.95 = 36.64N

12. The guy wire of two vertical electrical pole makes 40° with horizontal and subjected to 40 kN force. What will be the horizontal component of force? As shown in Fig.

(a) 30.64 kN (b) 0kN (c) 33.56 kN (d) 25.68 kN

Ans.: (b) Explanation : T = 40 kN q = 40° åFx = ‒40 cos 40° + 40 cos 40° = 0

13. Three forces 25 N, 50 N and 75 N act along AB, BC and CA respectively along the sides of an equilateral triangle. AB being horizontal. The resultant of the force system is _____.

(a) 37.50 N (b) 21.66 N (c) 43.30 N (d) 59.16 N

Ans.: (c) Explanation : åFx = 0 = ‒ 25 + 50 cos 60° + 75 cos 60° = 37.5 N åFy = 50 sin 60° – 75 sin 60° = ‒ 21.66 N R = (37.5)2 + (‒21.66)2 R = 43.30 N

14. The components of force of 200 N in direction inclined to it at 40° and 50° on opposite sides are ____.

(a) 128.55 N and 153.20 N (b) 153.20 N & 125.55 N (c) ‒128.55 N and ‒153.20 N (d) ‒153.20 N & ‒128.55 N

Ans.: (b) Explanation :  a = 40°b = 50°a + b = 40° + 50° = 90° Fx = F è æ ø ö sin b sin (a + b) = 200 ë é û ù sin 50 sin90 = 153.20 N Fy = F è æ ø ö sina sin (a + b) = 200 ë é û ù sin 40 sin90 = 125.55 N

15. Three forces 20 N, 30 N and 40 N act along sides of equilateral triangle taken in order. 20 N force is acting horizontally towards right. Their resultant is _____.

(a) 20 N (b) 17.32 N (c) 30 N (d) 40 N

Ans.: (b)