Dimensions of physical quantities, dimensional analysis and its applications - Question Bank

1. Which quantity has dimensions of ML^-1T^-1?
A) Coefficient of viscosity
B) Momentum
C) Impulse
D) Surface tension
2. The dimensions of electric flux are:
A) [M L^3 T^-3 A^-1]
B) [M L T^-2 A^-1]
C) [M L^2 T^-2 A]
D) [A L^2]
3. Dimensional analysis can be used to convert units from one system to another. For example, to convert 1 Newton to dyne, we use dimensions of force:
A) [M L T^-2]
B) [M L^2 T^-2]
C) [M L^-1 T^-2]
D) [M L T]
4. If the equation of state for an ideal gas is PV = nRT, what are the dimensions of R (the universal gas constant)?
A) [M L^2 T^-2 K^-1 mol^-1]
B) [M L T^-2]
C) [L^3]
D) [K]
5. The dimensions of angular acceleration are:
A) [T^-2]
B) [M L T^-2]
C) [L T^-2]
D) [M^0 L^0 T^0]
6. If the velocity of a wave is given by v = sqrt(T/rho), where T is tension and rho is linear density, this equation is dimensionally:
A) Correct
B) Incorrect
C) Depends on the units of T
D) Depends on the units of rho
7. Which of the following is a derived SI unit?
A) Meter
B) Ampere
C) Watt
D) Kelvin
8. The dimensions of surface energy are the same as those of:
A) Surface tension
B) Energy
C) Force
D) Pressure
9. If the force F = 6 pi eta r v, where eta is the coefficient of viscosity, r is the radius, and v is the velocity, what are the dimensions of eta?
A) [M L^-1 T^-1]
B) [M L T^-1]
C) [M L^-1 T^-2]
D) [M L T^-2]
10. The dimensions of magnetic field strength are:
A) [M T^-2 A^-1]
B) [M L T^-2 A^-1]
C) [M L^2 T^-2 A^-2]
D) [A]
11. If a quantity has dimensions [M^1 L^2 T^-2], it could represent:
A) Work or Energy
B) Force
C) Power
D) Momentum
12. The dimensions of torque are:
A) [M L^2 T^-2]
B) [M L T^-2]
C) [M L^2 T^-1]
D) [M L]
13. If the equation for the period of a simple pendulum T = 2 pi sqrt(l/g) is to be checked dimensionally, what are the dimensions of g (acceleration due to gravity)?
A) [L T^-2]
B) [L T^-1]
C) [M L T^-2]
D) [T]
14. If the equation for the period of a simple pendulum T = 2 pi sqrt(l/g) is to be checked dimensionally, what are the dimensions of l (length)?
A) [L]
B) [L^2]
C) [M]
D) [T]
15. The dimensions of the Stefan-Boltzmann constant are:
A) [M T^-3 K^-4]
B) [M L^2 T^-2 K^-1]
C) [M L T^-2]
D) [M^0 L^0 T^0]
16. Which of the following is NOT a valid application of dimensional analysis?
A) Finding the relationship between physical quantities
B) Checking the consistency of physical equations
C) Determining the exact form of a physical law
D) Converting units from one system to another
17. The dimensions of pressure gradient are:
A) [M L^-2 T^-2]
B) [M L^-1 T^-2]
C) [M L T^-2]
D) [M L^0 T^-2]
18. What are the dimensions of acceleration due to gravity?
A) [L T^-2]
B) [M L T^-2]
C) [L T^-1]
D) [M L^-1 T^-2]
19. If v = sqrt(P/rho), where v is velocity, P is pressure, and rho is density, this equation is dimensionally:
A) Correct
B) Incorrect
C) Cannot be determined
D) Correct only if P is force
20. The dimensions of coefficient of friction are:
A) [M^0 L^0 T^0]
B) [M L T^-1]
C) [M L T^-2]
D) [M L^-1 T^-2]
21. Which physical quantity has dimensions of [M L^2 T^-3]?
A) Energy
B) Power
C) Force
D) Momentum
22. The dimensions of the Boltzmann constant are the same as those of:
A) Energy per degree Kelvin
B) Force per meter
C) Work per second
D) Momentum per unit length
23. If the equation P = E / T is dimensionally correct, where P is power, E is energy, and T is time, what are the dimensions of P?
A) [M L^2 T^-3]
B) [M L T^-2]
C) [M L^2 T^-2]
D) [M L]
24. The dimensions of electric current are:
A) [A]
B) [C]
C) [V]
D) [Ohm]
25. Which of the following represents the dimensions of work done?
A) [M L^2 T^-2]
B) [M L T^-2]
C) [M L^2 T^-1]
D) [M L T^-1]
26. The dimensions of frequency are:
A) [T^-1]
B) [M L T^-1]
C) [L T^-2]
D) [M]
27. If the distance s is related to time t by s = a t^2 + b t + c, then the dimensions of c are:
A) [L T^-1]
B) [L]
C) [T]
D) [L T]
28. If the distance s is related to time t by s = a t^2 + b t + c, then the dimensions of b are:
A) [L T^-1]
B) [L]
C) [T]
D) [L T]
29. The dimensions of power are:
A) [M L^2 T^-3]
B) [M L T^-2]
C) [M L^2 T^-2]
D) [M L T^-3]
30. Which of the following quantities has dimensions of energy?
A) Force x Velocity
B) Force / Velocity
C) Force x Time
D) Force / Time
31. The dimensions of coefficient of viscosity are:
A) [M L^-1 T^-1]
B) [M L T^-1]
C) [M L^-1 T^-2]
D) [M L T^-2]
32. If E = mc^2, where E is energy, m is mass, and c is the speed of light, this equation is dimensionally:
A) Correct
B) Incorrect
C) Partially correct
D) Depends on the units used
33. What are the dimensions of Planck's constant (h)?
A) [M L^2 T^-1]
B) [M L T^-2]
C) [M L^2 T^-2]
D) [M L T^-1]
34. The dimensions of the universal gravitational constant G are:
A) [M^-1 L^3 T^-2]
B) [M L^3 T^-2]
C) [M^-1 L^2 T^-2]
D) [M L^3 T^-1]
35. Which of the following applications of dimensional analysis is INCORRECT?
A) To convert a unit from one system to another
B) To derive relation between different physical quantities
C) To check the dimensional correctness of an equation
D) To determine the value of physical constants
36. The dimensions of angular momentum are:
A) [M L^2 T^-1]
B) [M L T^-1]
C) [M L^2 T^-2]
D) [M L^-1 T^-1]
37. If the velocity of a particle is given by v = At + B, where v is in m/s and t is in seconds, then the dimensions of B are:
A) [L T^-2]
B) [L T^-1]
C) [L]
D) [T]
38. If the velocity of a particle is given by v = At + B, where v is in m/s and t is in seconds, then the dimensions of A are:
A) [L T^-2]
B) [L T^-1]
C) [L]
D) [T]
39. The dimensions of kinetic energy are:
A) [M L^2 T^-2]
B) [M L T^-2]
C) [M L^2 T^-1]
D) [M L T^-1]
40. Which of the following is a dimensionless quantity?
A) Refractive index
B) Velocity
C) Acceleration
D) Force
41. The dimensions of surface tension are:
A) [M T^-2]
B) [M L T^-2]
C) [M L^2 T^-2]
D) [M L^-1 T^-2]
42. Dimensional analysis is NOT applicable when the equation involves:
A) Addition or subtraction of physical quantities
B) Multiplication or division of physical quantities
C) Constants like pi or numerical factors
D) Trigonometric or exponential functions
43. What are the dimensions of angular velocity?
A) [T^-1]
B) [M L T^-1]
C) [L^2 T^-1]
D) [M^0 L^0 T^0]
44. The dimensions of impulse are the same as those of:
A) Momentum
B) Force
C) Work
D) Pressure
45. Which physical quantity has dimensions [M^0 L^0 T^0]?
A) Force
B) Energy
C) Strain
D) Power
46. The dimensions of pressure are:
A) [M L^-1 T^-2]
B) [M L T^-2]
C) [M L^2 T^-2]
D) [M^-1 L T^-2]
47. What are the dimensions of velocity?
A) [L T^-1]
B) [L T^-2]
C) [L^2 T^-1]
D) [M L T^-1]
48. Dimensional analysis can be used to check the:
A) Correctness of a physical equation
B) Magnitude of a physical quantity
C) Nature of a physical force
D) Direction of a vector quantity
49. The SI unit of force is Newton. What are its dimensions?
A) [M L T^-2]
B) [M L^2 T^-2]
C) [M L T]
D) [M L^-1 T^-2]
50. Which of the following is NOT a fundamental unit in the SI system?
A) Meter
B) Kilogram
C) Second
D) Newton
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