CHAPTER 2 VECTORS AND EQUILIBRIUM

 

2.1      Multiple choice questions.

1.      Which one of the following is a scalar quantity?
(a) Force	(b) Torque
(c) Momentum	(d) Density
2.      Which one of the following is a vector quantity?
(a) Work	(b) Power
(c) Weight	(d) Mass
3.      Which pair includes a scalar and a vector quantity?
(a) K.E. and momentum	(b) P.E. and Work
(c) Weight and force	(d) Velocity and acceleration
4.      Two vectors A1 and A2 are making an angle of 90° with each other What is Their resultant magnitude
(a) A12 + A22	(b)√(A1)2+ (A2)2
(c) √(A1)2+ (A2)2+ A1 A2	(d) √(A1)2+ (A2)2+ ½A1 A2
5.      The magnitude of two vectors is 3N and 4N respectively. If the angle between them is right angle, then their resultant vector will be:
(a) 5 N	(b) 6 N
(c) 7 N	(d) Zero
6.      At what angle the vertical component of a vector is maximum?
(a) 0°	(b) 30°
(c) 45°	(d) 90°
7.      In which quadrant a vector can be drawn when it’s both x and y components are negative
(a) First	(b) Second
(c) Third	(d) Fourth
8.   What is the possible result of (-3î)·(-4ĵ)?
(a) Zero	(b) One
(c) 12k̂	(d) 12
9.   What is the angle of the given vector 2î+2ĵ??
(a) 30°	(b) 45°
(c) 60°	(d) 90°
10. The correct result of the expression ĵ·(k̂×ĵ) is
(a) Zero	(b) One
(c) î	(d) ĵ
11.  Which law does not obey the vector product of two vectors?
(a) Associative	(b) Commutative
(c) Distributive	(d) Identitive
12.  The scalar product of two non-zero vectors is equal to zero when angle Between them is;
(a) 0°	(b) 30°
(c) 60°	(d) 90°
13.  The vector product of two vectors is maximum when both the vectors
(a) Parallel	(b) Anti-parallel
(c) Perpendicular	(d) Equal

14. What is the expected result of (A×B)²+(A·B)² = ?
(a) A2B2cos(θ)	(b) A2B2sin(θ)
(c) AB	(d) A2B2
15.  Self cross product of unit vectors is always
(a) One	(b) Zero
(c) Linear	(d) Non-linear
16. The magnitude of dot and cross products of two vectors are 6√3 and respectively, the angle between the vectors is:
(a) 90°	(b) 60°
(c) 30°	(d) Zero
17.  What torque is produced by 30N force is acting at 60° on a wrench of length 30 cm
(a) 5.8 Nm	(b) 6.8 Nm
(c) 7.8 Nm	(d) 8.8 Nm
18.  A force of 10N at 60° is acting on a block, what force in opposite direction will Bring to block at equilibrium.
(a) 5 N	(b) 10N
(c) 15N	(d) 100 N
19.  If the line of action of the force passes through their axis of rotation or origin, then its torque is.
(a) Zero	(b) Maximum
(c) One	(d) None of these

 

Answers

1. (d) Density
2. (c) Weight
3. (a) K.E. and momentum
4. (b) √(A₁)²⁺ (A₂)²
5. (a) 5 N
6. (d) 90°
7. (c) Third
8. (a) Zero
9. (b) 45°
10. (b) One
11. (b) Commutative
12. (d) 90°
13. (c) Perpendicular
14. (d) A²B²
15. (b) Zero
16. (c) 30°
17. (c) 7.8 Nm
18. (a) 5 N
19. (a) Zero

2.2      Short questions

10.      How scalar product of two vectors obeys commutative law?

ans

2.3      Numerical problems

4. What is the magnitude and direction of a vector when its horizontal component is doubled then its vertical?

14. A uniform beam of weight 40 N is subjected by forces as shown in figure. What is the magnitude, direction? And location of a force can be kept the beam in equilibrium?