DC Pandey Solutions: Units, Dimensions & Vectors - 1 Notes | Study Physics Class 11 - NEET

Section-I
Single Correct Option
Q.1. Which one of the following has the dimensions of pressure? 
(a) [ML^-2T^-2] 
(b) [M^-1 L^-1] 
(c) [MLT^-2] 
(d) [ML^-1T^-2]
Ans. (d)

Sol: 
∴
= [ML^-1T^-2]

Q.2. Which of the following will have the dimensions of time
(a) LC
(b) R/L
(c) L/R
(d) C/L
Ans. (c)

W = I² Rt
∴

∴

Using Eq. (i)
[R] = [L]/[T]
i.e., [T] = [L/R]
Option  is correct.

Q.3. The force F on a sphere of radius a moving in a medium with velocity v is given by F = 6πηa v. The dimensions of-η are
(a) [ML^-3] 
(b) [MLT^-2] 
(c) [MT^{- 1}] 
(d) [ML^-1T^-1]
Ans: (d)

F= 6π ηav
∴

Q.4. The dimensional formula for magnetic flux is
(a) [ML²T ^-2A^-1] 
(b) [ML³T^-2A^-2]
(c) [M⁰ L^-2T^-2A^-2] 
(d) [ML²T^-1A²]
Ans: (a)

φ = Li
∴  [φ] = [L] [i]
=[ML² T^-2 A^-2] [A]
=[ML² T^-2 A^-1]
Option  is correct.

Q.5. Dimensions of linear impulse are
(a) [ML^-2T^-3]
(b) [ML^-2]
(c) [MLT ^-1]
(d) [MLT^-2]
Ans. (c)

Linear impulse (I) = F × Δt
[I ] = [MLT^-2] [T]
= [MLT^-1]

Q.6. What is the dimensional formula of gravitational constant? 
(a) [ML²T^-2] 
(b) [ML^-1T ^-1] 
(c) [M^-1L³ T^-2] 
(d) None of these
Ans. (c)

Q.7.Using mass (M), length (L), time (T) and current (A) as fundamental quantities, the dimension of permeability is 
(a) [M^-1LT^-2A] 
(b) [ML^-2T^-2A^-1] 
(c) [MLT ^-2A^-2] 
(d) [MLT ^-1 A^-1]
Ans. (c) 

Q.8. The equation of a wave is given bywhere ω is angular velocity and v is the linear velocity. The dimensions of k will be 
(a) [T²] 
(b) [T^-1] 
(c) [T] 
(d) [LT]
Ans. (c)

Q.9. A force is given by F = at + bt²
where t is the time. The dimensions of a and b are
(a) [MLT ^-4] and [MLT ¹] 
(b) [MLT^-1] and [MLT⁰] 
(c) [MLT^-3] and [MLT ^-4] 
(d) [MLT ^-3] and [MLT⁰]
Ans. (c)

Q.10. The dimensional formula for Planck’s constant and angular momentum are
(a) [ML²T^-2] and [MLT^-1] 
(b) [ML²T^-1] and [ML²T^-1] 
(c) [ML³T¹] and [ML²T ^-2] 
(d) [MLT^-1] and [MLT^-2]
Ans. (b)

∴
Angular momentum (J) = nh/2π
[J] = [h] = [ML² T^-1]

Q.11. If the energy (E), velocity (v) and force (F) be taken as fundamental quantities, then the dimensions of mass will be
(a) Fv^-2 (b) Fv^-1 (c) Ev^-2 (d) Ev²
Ans. (c)

[Energy] = [ML²T^-2]
= -[M] [LT^-1]²
∴ [Mass] = [Ev^-2]
Option  is correct.

Q.12. The dimension of  (ε₀ is the permittivity of free space and E is electric field), is 
(a) [ML²T^-1] 
(b) [ML^{- 1}T^-2] 
(c) [ML²T^-2] 
(d) [MLT^-1]
Ans. (b)

  = Energy density = Energy/Volume
 ∴
= [ML^-1 T^-2]

Q.13. The dimensions of a/b in the equation  where P is pressure, x is distance and t is time, are 
(a) [M² LT ^-3] 
(b) [MT^-2] 
(c) [LT^-3] 
(d) [ML³ T^-1]
Ans. (b)

Sol: [a] = [T²]

∴

Q.14. Dimension of velocity gradient is
(a) [M°L°T^-1] 
(b) [ML^{- 1}T^-1] 
(c) [M°LT^-1] 
(d) [ML°T^-1]
Ans. (a)

Sol: Velocity gradient = dv/dx
[Velocity gradient]
= [T^-1]
= [M⁰ L⁰ T^-1]

Q.15. If force F, length Land time T are taken as fundamental units, the dimensional formula for mass will be 
(a) [FL^{- 1}T²] 
(b) [FLT^-2] 
(c) [FL^{- 1}T^-1] 
(d) [FL⁵T²]
Ans: (a)

[Force] = [MLT^-2]

Q.16. Which of the following is the dimension of the coefficient of friction? (a) [M² L²T] 
(b) [M° L° T°] 
(c) [ML²T^-2] 
(d) [M² L²T^-2]
Ans. (b)

Sol: Coefficient of friction (μ)

∴   [μ] = [M⁰ L⁰ T⁰]
Option  is correct.

Q.17. If C and R denote capacitance and resistance, then dimensions of CR will be 
(a) [M°L°TA°] 
(b) [ML°TA^-2] 
(c) [ML°TA²] 
(d) [ML°T²A^-2]
Ans: (a)

q = CV
and V = iR
∴ q = iCR
it = iCR
⇒ [CR] = [t] = [M⁰ L⁰ T A⁰]

Q.18. The unit of permittivity of free space, ε₀ is
(a) coulomb/newton-metre
(b) newton-metre²/coulomb²  
(c) coulomb²/newton-metre²
(d) coulomb² /(newton -metre)²
Ans: (b)

∴ Unit of ε₀ = Newton-metre² /coulomb².

Q.19. The ratio of the dimensions of Planck’s constant and that of the moment of inertia is the dimension of 
(a) frequency 
(b) velocity 
(c) angular momentum 
(d) time
Ans. (a)

Angular momentum (J) = nh/2π
∴

Q.20. The velocity v of a particle at time t is given by  where a, b and c are constants. The dimensions of a, b and c are respectively
(a) [LT^-2], [L] and [T]
(b) [L²], [T] and [LT²]
(c) [LT²], [LT] and [L]
(d) [L], [LT] and [T²]
Ans. (a)

[c] = [T]

or [b] = [LT^-1] [T] = [L]
[at] = [v] = [LT^-1]
⇒ [a] = [LT^-2]

Q.21. Given that  where y and x are measured in metres. Which of the following statements is true ? 
(a) The unit of λ is same as that of x and A
(b) The unit of λ, is same as that of x but not of A
(c) The unit of c is same as that of 2π/λ
(d) The unit of (ct - x) is same as that of 2π/λ
Ans. (a)

∴ [x] = [λ] = [L] 
Further, y = A sinθ
∴ [A] = [y] = [L]

Q.22. The physical quantity having the dimensions [M^-1L^-3T³A²] is 
(a) resistance 
(b) resistivity 
(c) electrical conductivity 
(d) electromotive force
Ans. (a)

[X] = [M^-1 L^-3 T³ A²]


∴ X is resistance.  [∴W = i² Rt]

Q.23. The torque of force  newton acting at the point  metre about origin is (in N-m)
(a)
(b)
(c)
(d)
Ans. (b)

Q.24. If a unit vector is represented by  the value of c is
(a) 1
(b) √0.11
(c) √0.01

(d) 0.39
Ans: (b)

Q.25.  are two vectors such that  he angle between vectors is

Ans. 

Q.26. The vector sum of two forces is perpendicular to their vector differences. In that case, the forces 
(a) are not equal to each other in magnitude 
(b) cannot be predicted 
(c) are equal to each other 
(d) are equal to each other in magnitude
Ans. (d)

Q.27. Which one of the following is a scalar quantity? 
(a) Displacement 
(b) Electric field 
(c) Acceleration 
(d) Work
Ans: (d)

Work  is a scalar quantity.

Q.28. Which one of the following is not the vector quantity? 
(a) Torque 
(b) Displacement 
(c) Velocity 
(d) Speed
Ans: (d)

Q.29. What is the dot product of two vectors of magnitude 3 and 5, if angle between them is 60°? 
(a) 5.2 
(b) 7.5 
(c) 8.4 
(d) 8.6
Ans: (b)

 and angle between is 60°.
∴

= 7.5

Q.30. Two vectors   are such that   and A² + B² = C².
If 0 is the angle between positive direction of  then the correct statement is  
(a) θ = π
(b) θ = 2π/3
(c) θ = 0
(d) θ = π/2
Ans: (d)

∴
or
or
or
or
or cos θ = 0
or θ = π/2