11th Physics MCQs Preparation 2022 and Onwards (Unit: Vectors and Equilibrium: Set-1 (34 MCQs)) for ECAT, FPSC, PPSC, JOB Exam, Physics Lecturer, SSC, HSSC (F.Sc.), BS, MS Exams NTS, ETS, etc.
1. Which one of the following is a scalar quantity?
--------------------------
2. Which one of the following is a vector quantity?
----------------------
3. Which pair includes a scalar and a vector quantity?
---------------------------
4. Two vectors `\vec A_1` and `\vec A_2` are making an angle of 90° with each other. What is their resultant magnitude?
--------------------------------
5. The magnitude of the two vectors is 3N and 4N respectively. If the angle bet them is 90°, then their resultant vector will be:
By using Pythagoras' theorem
------------------------------
--------------------------
-------------------------
θ = tan⁻¹ (Ay/Ax) = tan⁻¹ (2/2) = tan⁻¹ (1) = 45°
----------------------
------------------------------
-------------------------
By using Pythagoras' theorem
6. At what angle the vertical component of a vector is maximum?
------------------------------
7. In which quadrant a vector can be drawn when its both x and y components are negative. :
--------------------------
8. What is the possible result of (-3`\hat i`).(-4`\hat j`)
-------------------------
9. What is the angle of the given vector 2`\hat i`+2`\hat j`?
θ = tan⁻¹ (Ay/Ax) = tan⁻¹ (2/2) = tan⁻¹ (1) = 45°
10. The correct result of the expression `\hat j`.(`\hat k` x `\hat i`) is:
----------------------
11. Which law does not obey the vector product of two vectors?
------------------------------
12. The scalar product of two non-zero vectors is equal to zero when the angle between them is;
-------------------------
13. The vector product of two vectors is maximum when both vectors are
θ = 0° and sin 0° = 1
----------------------------
`\vec A` X `\vec A` = 0
A.B = AB cosθ = 6√3 ...(1), A×B = AB sinθ = 6 ......(2)⇒ Dividing (2) by (1)⇒ tanθ = 1/√3 = 30°
r= 30 cm = 0.3 m, θ = 60° and f = 30N ⇒ T = r x F = r F sin θ = 0.3m x 30N x sin 60° = 7.8 N m
∑F= 0
T = r x F = r F sin θ, when r = 0 then T = 0
Clockwise Torque = r x F = 2m x 10 N = 20 N m 👉 Anticlockwise Torque = 2 m x 5 N = 10 N m 👉 difference 20 -10 = 10 N m 👉 Clockwise torque dominate 10 N m. So the correct option is C.
Sin ( 45° ) = cos ( 45° ) = 0.707
...
Answer is C. 
Option C is an equilibrium. All other options produce torque
Σꓔ = 0 👉 m x (14 - 30 cm) + 80 g x 20 cm = 0 👉 m x (-16 cm) + 1600 g cm = 0 👉 m x (16 cm) - 1600 g cm 👉 m = 100 g
Let the minimum force is F 👉 then the larger force will be 16 - F 👉 the resultant and minimum force are perpendicular to each other. 👉 So, R = 8 = √ (F)² + (16 - F)² 👉 By solving we get F = 6 N (minimum force) 👉 Larger force 16 - F = 16 - 6 = 10 N.
θ = 0° and sin 0° = 1
14. What is the expected result of (`\vec A` X `\vec B`)² + (`\vec A` . `\vec B`)² = ?
----------------------------
15. Self cross product of unit vectors is always
`\vec A` X `\vec A` = 0
16.. The magnitude of the dot and cross products of two vectors are 6`\sqrt 3` respectively, and the angle between the vectors is:
A.B = AB cosθ = 6√3 ...(1), A×B = AB sinθ = 6 ......(2)⇒ Dividing (2) by (1)⇒ tanθ = 1/√3 = 30°
17. What torque is produced by 30 N force which is acting at 60° on a wrench of length 30 cm? :
r= 30 cm = 0.3 m, θ = 60° and f = 30N ⇒ T = r x F = r F sin θ = 0.3m x 30N x sin 60° = 7.8 N m
18. A force of 1O N at 60° is acting on a block, what force in opposite direction will bring to block at equilibrium.
∑F= 0
19. If the line of action of the force passes through its axis of rotation or origin, then its torque is:
T = r x F = r F sin θ, when r = 0 then T = 0
20. What is the net torque on wheel radius 2 m as shown?
Clockwise Torque = r x F = 2m x 10 N = 20 N m 👉 Anticlockwise Torque = 2 m x 5 N = 10 N m 👉 difference 20 -10 = 10 N m 👉 Clockwise torque dominate 10 N m. So the correct option is C.
21. For which angle the equation |`\vec {A}` • `\vec {B}`| = |`\vec {A}` X `\vec {B}`| is correct.
Sin ( 45° ) = cos ( 45° ) = 0.707
22. The following diagrams show a uniform rod with its midpoint on the pivot. Two equal forces Fare applied on the rod, as shown in the Which diagram shows the rod in equilibrium?
...
Answer is C. Option C is an equilibrium. All other options produce torque
23. Find the mass of the uneven rod shown in the figure. If its gravity is 14 cm from end A is_______ :
Σꓔ = 0 👉 m x (14 - 30 cm) + 80 g x 20 cm = 0 👉 m x (-16 cm) + 1600 g cm = 0 👉 m x (16 cm) - 1600 g cm 👉 m = 100 g
24. The sum of the magnitudes of two forces is 16 N. If the resultant is 8 N and its direction is perpendicular to the minimum force then the forces are
Let the minimum force is F 👉 then the larger force will be 16 - F 👉 the resultant and minimum force are perpendicular to each other. 👉 So, R = 8 = √ (F)² + (16 - F)² 👉 By solving we get F = 6 N (minimum force) 👉 Larger force 16 - F = 16 - 6 = 10 N.
25. If the dot product of two nonzero vectors A and B is zero then the magnitude of their cross product is _________.
When two vectors are perpendicular to each other then their dot product is zero and the cross product is equal to the product of the magnitude of both vectors. So, the correct option is C. AB
The magnitude of the resultant vector should always be greater than the magnitude of any individual vector. As 20 N is less than both of the given vectors So, option A is the correct answer.
The Cross Product of two vectors A and B gives a vector that is perpendicular to both vectors (A and B). Let A x B = C. Thus A and C are perpendicular to each other. So their dot product will be equal to zero.
Ax is Positive and Ay is negative so it lies in IV quadrant
Σꓔ = 0 👉 4 N x (50 - 20 cm) + 6 N x (50 - 80 cm) + 3 N x X = 0 👉 120 N cm - 180 N cm + 3 N x X = 0 👉 - 60 N cm + 3 N x X = 0 👉 3 N x X = 60 N cm 👉 X = 20 cm
| F | = √ ( Fᵪ² + Fᵧ² ) 👉 5 N = √ ( (3 N)² + Fᵧ²) 👉 by taking square both side 👉 25 N² = 9 N² + Fᵧ² 👉 Fᵧ² = 25 N² - 9 N² 👉 Fᵧ² = 16 N² 👉 by taking square root both side we get Fᵧ = 4 N
When two vectors are perpendicular to each other then their dot product is zero and the cross product is equal to the product of the magnitude of both vectors. So, the correct option is C. AB
26. Two forces of magnitude 20 N and 50 N act simultaneously on a body. Which one of the following forces cannot be a result of the two forces?
The magnitude of the resultant vector should always be greater than the magnitude of any individual vector. As 20 N is less than both of the given vectors So, option A is the correct answer.
27. `\vec {A}` • (`\vec {A}` X `\vec {B}`) = ? :
The Cross Product of two vectors A and B gives a vector that is perpendicular to both vectors (A and B). Let A x B = C. Thus A and C are perpendicular to each other. So their dot product will be equal to zero.
28. If `\vec {A}`x = 1.5 cm, `\vec {A}`y =-1.0 cm, into which quadrant do the vector `\vec {A}` point? :
Ax is Positive and Ay is negative so it lies in IV quadrant
29. A meter stick is supported by a knife edge at the 50-cm mark. Arif hangs masses of 0.40 kg and 0.60 kg from the 20 cm and 80 cm marks, respectively. Where should Arif hang a third mass of 0.30 kg to keep the stick balanced?
Σꓔ = 0 👉 4 N x (50 - 20 cm) + 6 N x (50 - 80 cm) + 3 N x X = 0 👉 120 N cm - 180 N cm + 3 N x X = 0 👉 - 60 N cm + 3 N x X = 0 👉 3 N x X = 60 N cm 👉 X = 20 cm
30. When Fᵪ = 3 N and F=5 N then Fᵧ =
| F | = √ ( Fᵪ² + Fᵧ² ) 👉 5 N = √ ( (3 N)² + Fᵧ²) 👉 by taking square both side 👉 25 N² = 9 N² + Fᵧ² 👉 Fᵧ² = 25 N² - 9 N² 👉 Fᵧ² = 16 N² 👉 by taking square root both side we get Fᵧ = 4 N
31. The magnitude of vector `\vec {A}`= 2`\hat {i}` + `\hat {j}` + 2`\hat {k}`
|A| = √ ( 2² + 1² + 2²) = √ ( 4 + 1 + 4 ) = √ (9) = 3
---------------
Adding three unequal vectors like a scalene triangle will give a zero resultant.
A • B = AB cos (80°) = 0.174 AB and when increased by 20° i.e. 80° + 20° = 100° 👉 A • B = AB cos (100°) = - 0.174 AB 👉 Both are of the same magnitude but one with a negative sign.
|A| = √ ( 2² + 1² + 2²) = √ ( 4 + 1 + 4 ) = √ (9) = 3
32. If the resultant of two vectors, each of magnitude A is also a magnitude of A. the angle between the two vectors will be:
---------------
33. The minimum number of vectors of the unequal magnitude required to produce a zero resultant is
Adding three unequal vectors like a scalene triangle will give a zero resultant.
34. Two vectors lie with their tails at the same point. When the angle between them is increased by 20° their scalar product has the same magnitude but changes from positive to negative. The original angle between them was:
A • B = AB cos (80°) = 0.174 AB and when increased by 20° i.e. 80° + 20° = 100° 👉 A • B = AB cos (100°) = - 0.174 AB 👉 Both are of the same magnitude but one with a negative sign.
************************************
Or