HSSC-1 (Class-11) Solved Physics MCQs; Unit-2: Vectors and Equilibrium;  (New Book/KPK Text Board, Peshawar) With Verified Answers 


1. 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:



... Answer is D. 80°
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.


2. The minimum number of vectors of the unequal magnitude required to produce a zero resultant is




... Answer is B. 3
Adding three unequal vectors like a scalene triangle will give a zero resultant. 


3. If the resultant of two vectors, each of magnitude A is also a magnitude of A. the angle between the two vectors will be:




... Answer is D. 120°



4. The magnitude of vector `\vec {A}`= 2`\hat {i}` + `\hat {j}` + 2`\hat {k}`




... Answer is C. 3
|A| = √ ( 2² + 1² + 2²) = √ ( 4 + 1 + 4 ) = √ (9) = 3


5. When Fᵪ = 3 N and F=5 N then Fᵧ =




... Answer is B.  4 N
| 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


6. 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?




... Answer is A. 20 cm
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


7. If `\vec {A}`x = 1.5 cm, `\vec {A}`y =-1.0 cm, into which quadrant do the vector `\vec {A}` point? :




... Answer is D. IV
Ax is Positive and Ay is negative so it lies in IV quadrant


8. `\vec {A}` • (`\vec {A}` X `\vec {B}`) = ?




... Answer is A. 0
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.


9. 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?




... Answer is A. 20 N
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.


10. If the dot product of two nonzero vectors A and B is zero then the magnitude of their cross product is _________.




... Answer is C. AB
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


11. 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




... Answer is A. 6 N and 10 N
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.


12. Find the mass of the uneven rod shown in the figure. If its gravity is 14 cm from end A is_______ :







... Answer is A. 100 g
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


13. 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


14. For which angle the equation |`\vec {A}` • `\vec {B}`| = |`\vec {A}` X `\vec {B}`| is correct.




... Answer is B. 45°
Sin ( 45° ) = cos ( 45° ) = 0.707


15. What is the net torque on wheel radius 2 m as shown? 



     A. 



... Answer is C. 10 N m clockwise
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.



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