PRACTICE SHEET # 02-B (SCALARS AND VECTORS)
1. The angle between rectangular components of a vector is:
a. 0 b. 60 c. 90 d. 120
2. A force of 10N is acting along y-axis its component along x-axis is:
a. 10N b. 20N c. 100N d. Zero N
3. Two forces are acting together on an object. The magnitude of their resultant is minimum when the angle
between the force is:
a. 0 b. 60 c. 120 d. 180
4. Two forces of 10N and 15N are acting simultaneously on an object in the same direction. Their resultant is:
a. Zero b. 5N c. 25N d. 150N
5. Three forces 9, 12 and 15 N acting on a point are in equilibrium. The angle between 9 N and 15 N is:
3 4 3 4
a. cos −1 (5) b. cos −1 (5) c. π − cos−1 (5) d. π − cos −1(5)
6. A boat which has a speed of 5km/h in still water crosses a river of width 1km along the shortest path in 15
minutes. The velocity of the river in km/hr is:
a. 1 b. 3 c. 4 d. √41
7. The magnitudes of vectors ⃗⃗⃗𝐀 , ⃗⃗⃗𝐁 and ⃗⃗⃗𝐂 are 3, 4 and 5 units respectively. If 𝐀 ⃗ +𝐁
⃗ = 𝐂 the angle between 𝐀 ⃗
and 𝐁⃗ is:
a. π/2 b. cos-1 0.6 c. tan-1 7/5 d. π/4
8. The magnitudes of vectors ⃗⃗⃗𝐀 , ⃗⃗⃗𝐁 and ⃗⃗⃗𝐂 are 6, 8 and 10 units respectively. If 𝐀 ⃗ +𝐁
⃗ = 𝐂 the angle between 𝐀 ⃗
and 𝐁⃗ is:
a. π/2 b. cos-1 0.6 c. tan-1 7/5 d. π/4
9. If two non-zero vectors ⃗⃗⃗𝐀 and ⃗⃗⃗𝐁 obey the relation | ⃗⃗⃗𝐀 + ⃗⃗⃗𝐁| = |⃗⃗⃗𝐀 – ⃗⃗⃗𝐁|, then the angle between them is:
a. 120o b. 90o c. 60o d. 0o
10. Five equal forces of 10N each are applied at one point and all are lying in one plane. If the angles between
them are equal the resultant force will be:
a. Zero b. 10N c. 20N d. 10 √2N
11. The sum of two forces acting at a point is 16N. If the resultant force is 8N and its direction is perpendicular
to minimum force then the forces are:
a. 6N and 10N b. 8N and 8N c. 4N and 12N d. 2N and 14N
12. The magnitude of vector ⃗⃗⃗𝐀 , ⃗⃗⃗𝐁 and ⃗⃗⃗𝐂 are respectively 12, 5 and 13 units and ⃗⃗⃗𝐀 + ⃗⃗⃗𝐁 = ⃗⃗⃗𝐂 then the angle
between ⃗⃗⃗𝐀 and ⃗⃗⃗𝐁 is:
a. 0 b. π c. π/2 d. π/4
13. If resultant of two forces (F and F) acting on a point is F, then the angle between two forces is:
a. 0o b. 45o c. 60o d. 120o
14. A boy walks uniformly along the sides of a rectangular park of size 400 m x 300 m, starting from one corner
to the other corner diagonally opposite. Which of the following statements is incorrect?
a. He has traveled a distance of 700 m
b. His displacement is 700 m
c. His displacement is 500 m
d. His velocity is uniform throughout the walk
15. Which pair of the following forces will never give resultant force of 2N?
a. 2N and 2N b. 1N and 1N c. 1N and 3N d. 1N and 4N
16. Two forces 3N an 2N are at an angle 𝛉 such that the resultant is R. The first force is now increased to 6N
and the resultant becomes 2R. The value of 𝛉 is:
a. 30o b. 60o c. 90o d. 120o
FROM THE DESK OF: ENGR. M. BILAL ZIA
1. The angle between rectangular components of a vector is:
a. 0 b. 60 c. 90 d. 120
2. A force of 10N is acting along y-axis its component along x-axis is:
a. 10N b. 20N c. 100N d. Zero N
3. Two forces are acting together on an object. The magnitude of their resultant is minimum when the angle
between the force is:
a. 0 b. 60 c. 120 d. 180
4. Two forces of 10N and 15N are acting simultaneously on an object in the same direction. Their resultant is:
a. Zero b. 5N c. 25N d. 150N
5. Three forces 9, 12 and 15 N acting on a point are in equilibrium. The angle between 9 N and 15 N is:
3 4 3 4
a. cos −1 (5) b. cos −1 (5) c. π − cos−1 (5) d. π − cos −1(5)
6. A boat which has a speed of 5km/h in still water crosses a river of width 1km along the shortest path in 15
minutes. The velocity of the river in km/hr is:
a. 1 b. 3 c. 4 d. √41
7. The magnitudes of vectors ⃗⃗⃗𝐀 , ⃗⃗⃗𝐁 and ⃗⃗⃗𝐂 are 3, 4 and 5 units respectively. If 𝐀 ⃗ +𝐁
⃗ = 𝐂 the angle between 𝐀 ⃗
and 𝐁⃗ is:
a. π/2 b. cos-1 0.6 c. tan-1 7/5 d. π/4
8. The magnitudes of vectors ⃗⃗⃗𝐀 , ⃗⃗⃗𝐁 and ⃗⃗⃗𝐂 are 6, 8 and 10 units respectively. If 𝐀 ⃗ +𝐁
⃗ = 𝐂 the angle between 𝐀 ⃗
and 𝐁⃗ is:
a. π/2 b. cos-1 0.6 c. tan-1 7/5 d. π/4
9. If two non-zero vectors ⃗⃗⃗𝐀 and ⃗⃗⃗𝐁 obey the relation | ⃗⃗⃗𝐀 + ⃗⃗⃗𝐁| = |⃗⃗⃗𝐀 – ⃗⃗⃗𝐁|, then the angle between them is:
a. 120o b. 90o c. 60o d. 0o
10. Five equal forces of 10N each are applied at one point and all are lying in one plane. If the angles between
them are equal the resultant force will be:
a. Zero b. 10N c. 20N d. 10 √2N
11. The sum of two forces acting at a point is 16N. If the resultant force is 8N and its direction is perpendicular
to minimum force then the forces are:
a. 6N and 10N b. 8N and 8N c. 4N and 12N d. 2N and 14N
12. The magnitude of vector ⃗⃗⃗𝐀 , ⃗⃗⃗𝐁 and ⃗⃗⃗𝐂 are respectively 12, 5 and 13 units and ⃗⃗⃗𝐀 + ⃗⃗⃗𝐁 = ⃗⃗⃗𝐂 then the angle
between ⃗⃗⃗𝐀 and ⃗⃗⃗𝐁 is:
a. 0 b. π c. π/2 d. π/4
13. If resultant of two forces (F and F) acting on a point is F, then the angle between two forces is:
a. 0o b. 45o c. 60o d. 120o
14. A boy walks uniformly along the sides of a rectangular park of size 400 m x 300 m, starting from one corner
to the other corner diagonally opposite. Which of the following statements is incorrect?
a. He has traveled a distance of 700 m
b. His displacement is 700 m
c. His displacement is 500 m
d. His velocity is uniform throughout the walk
15. Which pair of the following forces will never give resultant force of 2N?
a. 2N and 2N b. 1N and 1N c. 1N and 3N d. 1N and 4N
16. Two forces 3N an 2N are at an angle 𝛉 such that the resultant is R. The first force is now increased to 6N
and the resultant becomes 2R. The value of 𝛉 is:
a. 30o b. 60o c. 90o d. 120o
FROM THE DESK OF: ENGR. M. BILAL ZIA
