CBSE Class 11 Physics Units Dimensions Vectors Objective Questions

1. The only pair of physical quantities that does not have identical dimensions are
(a) angular momentum and Planck’s constant (b) torque and energy
(c) moment of inertia and moment of force (d) impulse and momentum

2. The dimensions of the quantities in one of the following pairs are the same. Identify the pair.
(a) angular momentum and energy (b) torque and work
(c) energy and Young’s modulus (d) light year and frequency

3. The dimensional formula for gas constant is
(a) [M⁰ L² T^–2 K^–2 mol^–1] (b) [M² L³ T^–1 K^–2 mol^–1]
(c) [M L⁰ T^–2 K^–3 mol^–1] (d) [M L² T^–2 K^–1 mol^–1]

4. The velocity of sound v in gas is v =√γ P/ ρ  where P is the pressure and ρ is density of the gas. The dimensional formula for γ is

(a) [M⁰ L⁰ T⁰] (b) [M⁰ L¹ T²] (c) [M¹ L² T⁰] (d) [M¹ L¹ T⁰]
5. The vectors A and B are such that |A + B| = |A – B|, the angle between these two vectors is
(a) 0º (b) 30º (c) 90º (d) 180º

6. If B + C = A and A = B = C, the angle between vectors B and C is
(a) 30º (b) 90º (c) 120º (d) 180º

7. If a force F = 2i + 5k Newton acts through a displacement s = 3j + 4k, work done is equal to
(a) 20 J (b) 26 J (c) 29 J (d) 39 J

8. If a force F = 8i – 20j Newton acts at the rim of a disc rotating at a distance r = –10i – 8j m from its centre, its torque T = r × F is equal to
(a) –80 N.m (b) 80 N.m (c) –264 N.m (d) 264 N.m

9. It is given that P + Q = R, R is perpendicular to P and |P| = |R|, the angle between P and Q is
(a) π/4  (b) π/2  (c) 3π/4  (d) π

10. A vector is not changed if
(a) it is multiplied to an arbitrary scalar (b) it is rotated through an arbitrary angle
(c) it is cross multiplied by a unit vector (d) it is slid parallel to itself.

11. If A = 4i – 2j + 6k and B = i – 2j – 3k, the angle which A + B makes with x-axis is
(a) Zero (b)  π/3  (c) π/4  (d) π/ 6

12. The coordinates of a particle moving at any time t is given by x = 2At² and y = 2Bt² where A and B are constants. The speed of the particle is
(a) 4t (A + B) (b) 4t √A² + B² (c) 4t (A² + B²) (d) 2t √A² + B²

13. A particle is moving eastwards with a velocity of 10 m/s. Its velocity change to 10 m/s northwards in 20s. The average acceleration in this time is
(a) 1/√2 m/s² towards north east (b) 1/√2 m/s² towards north west(c) 1/2  m/s² towards north west (d) 1 m/s2 towards north east
14. The position vector of a particle changes from 10 m east to 10 m north in 2 seconds. The averge velocity of the particle is

(a) 20 m/s (b) 5 m/s (c) 10 √2 m/s (d) 5 √2 m/s

15. ò  dx/√2ax-x²=  aⁿsin ^-1[x/a-1 ^] The value of n is

(a) 0 (b) –1 (c) 1 (d) none of these.

16. A physical quantity is measured and the result is expressed as nu where u is the unit used and n is the numerical value. If the result is expressed in various units then
(a) n ∝ size of u (b) n ∝ u² (c) n ∝ √u (d) n ∝ 1/u
17. A vector ar is turned through θ about its initial point. |Δ ar | of the vector is
(a) 0 (b) 2| a |θ (c) 2| a |sin θ/2 (d) 2| a |cos θ/2

18. The component of the vector j ˆ iˆ A = 2 + 3 ralong the vector j ˆ iˆ + is
(a) 5 (b) 5√2 (c) 10√2 (d) 2 √5

19. Suppose a quantity x can be dimensionally represented in terms of M, L and T, that is, [x] = Ma LbTc. The quantity mass
(a) can always be dimensionally represented in terms of L, T and x,
(b) can never be dimensionally represented in terms of L, T and x,
(c) may be represented in terms of L, T and x if a = 0,
(d) may be represented in terms of L, T and x if a ≠ 0.

20. A unitless quantity
(a) never has a nonzero dimension, (b) always has a nonzero dimension,
(c) may have a nonzero dimension (d) does not exist

21. The magnitude of i + j + k is
(a) 6 (b) 3 (c) 1 (d) 3

22. Two forces F1 and F2 are acting at right angles to each other. Then their resultant is
(a) F₁ + F₂ (b) √F₁² + F₂²  (c) √F₁² -  F₂²  (d) F₁ + F₂/2

23. The x and y components of a force are 2N and –3N. The force is
(a) 2i – 3j (b) 2i + 3j (c) –2i – 3j (d) 3i + 2j

24. Which of the following quantities are dependent on the choice of coordinate axes?
(a) a + b (b) a – b (c) a × b (d) ax + by

25. The angle between i + j + k and 2i + 2j + 2k is
(a) 0° (b) 30° (c) 60° (d) 90°

26. Identify the vector quantity
(a) work (b) time (c) heat (d) angular momentum

Objectives
1. (c) 2. (b) 3. (d) 4. (a) 5. (c) 6. (c) 7. (a) 8. (d) 9. (c) 10. (d) 11. (c) 12. (b) 13. (b) 14. (d) 15. (a) 16. (d) 17. (c) 18. (b) 19. (d) 20. (a) 21. (d) 22. (b) 23. (a) 24. (d) 25. (a) 26. (d)