Errors in measurements and dimensional analysis - Question Bank

1. If a quantity 'x' depends on 'y' and 'z' as x = y^n * z^m, the relative error in x is given by:
A) n(Δy/y) + m(Δz/z)
B) n(Δy/y) - m(Δz/z)
C) (Δy/y) + (Δz/z)
D) n(Δy/y) * m(Δz/z)
2. The dimensions of Stefan's constant are:
A) [M T^-3 K^-4]
B) [M L^2 T^-3 K^-4]
C) [M L T^-3 K^-4]
D) [M T^-2 K^-4]
3. If the error in measuring the diameter of a wire is 1%, what is the error in measuring its radius?
A) 0.5%
B) 1%
C) 2%
D) 0.25%
4. The dimensions of angular acceleration are:
A) [T^-2]
B) [L T^-2]
C) [M T^-2]
D) [M L T^-2]
5. Which of the following is a derived unit?
A) Ampere
B) Kelvin
C) Mole
D) Watt
6. If the percentage errors in the measurement of mass and velocity are 2% and 3% respectively, the maximum percentage error in the kinetic energy (KE = 1/2 mv^2) is:
A) 5%
B) 8%
C) 11%
D) 12%
7. The dimensions of the universal gas constant (R) are:
A) [M L^2 T^-2 K^-1]
B) [M L^2 T^-2]
C) [M L T^-2 K^-1]
D) [M L^2 T^-1 K]
8. A measurement has an error of ±0.5 units. If the measured value is 10.0 units, what is the percentage error?
A) 0.5%
B) 5%
C) 10%
D) 2%
9. If the period of oscillation of a simple pendulum is given by T = 2π√(l/g), where l is length and g is acceleration due to gravity, then the dimensions of g are:
A) [L T^-2]
B) [L T^-1]
C) [L^2 T^-2]
D) [M L T^-2]
10. 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^2 T^-1]
11. Which of the following is NOT a fundamental unit in the SI system?
A) Meter
B) Kilogram
C) Second
D) Newton
12. If measurements of length and time are made with an accuracy of ±1% and ±2% respectively, what is the accuracy in the calculation of velocity (v = l/t)?
A) ±1%
B) ±2%
C) ±3%
D) ±4%
13. The dimensions of work done are the same as:
A) Power
B) Momentum
C) Energy
D) Force
14. Which of the following is a unit of energy?
A) Watt
B) Joule
C) Newton
D) Pascal
15. The dimensions of the gravitational constant (G) are:
A) [M^-1 L^3 T^-2]
B) [M L^3 T^-2]
C) [M^-1 L^-3 T^-2]
D) [M L T^-2]
16. 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]
17. The dimensions of Planck's constant (h) are:
A) [M L^2 T^-1]
B) [M L T^-1]
C) [M L^2 T^-2]
D) [M L^-1 T^-1]
18. If the error in measuring the velocity of a particle is 3%, what is the error in measuring its kinetic energy?
A) 3%
B) 6%
C) 9%
D) 1.5%
19. The error in measuring the side of a cube is 2%. What is the maximum percentage error in its volume?
A) 2%
B) 4%
C) 6%
D) 8%
20. If the error in measuring the radius of a circle is 1%, what is the error in measuring its area?
A) 1%
B) 2%
C) 0.5%
D) 4%
21. Dimensional analysis cannot be used to:
A) Derive relations between physical quantities
B) Check the dimensional correctness of an equation
C) Convert units from one system to another
D) Determine the value of dimensionless constants
22. The principle of homogeneity of dimensions states that:
A) Dimensions of each term in an equation must be different
B) Dimensions of each term in an equation must be the same
C) Dimensions of only the first term must be checked
D) Dimensions are irrelevant in physical equations
23. If a quantity 'Q' is measured as x ± Δx, then Δx represents:
A) The true value of Q
B) The relative error in Q
C) The absolute error in Q
D) The percentage error in Q
24. The dimensions of surface tension are:
A) [M T^-2]
B) [M L T^-2]
C) [M L^2 T^-2]
D) [L T^-2]
25. The dimensions of impulse are:
A) [M L T^-1]
B) [M L T^-2]
C) [M L^2 T^-1]
D) [M L^-1 T^-1]
26. The dimensions of angular velocity are:
A) [T^-1]
B) [M T^-1]
C) [L T^-1]
D) [M L T^-1]
27. Which of the following is a dimensionless quantity?
A) Strain
B) Force
C) Velocity
D) Acceleration
28. The dimensions of density are:
A) [M L^-3]
B) [M L^3]
C) [M^-1 L^3]
D) [M L^-1]
29. The dimensions of pressure are:
A) [M L^-1 T^-2]
B) [M L T^-2]
C) [M L^2 T^-2]
D) [L T^-2]
30. The dimensions of energy are:
A) [M L^2 T^-2]
B) [M L T^-2]
C) [M L^2 T^-1]
D) [M L^-1 T^-2]
31. The dimensions of force are:
A) [M L T^-2]
B) [M L^-1 T^-2]
C) [M L^2 T^-2]
D) [M L T]
32. The dimensions of acceleration are:
A) [L T^-2]
B) [L T^-1]
C) [M L T^-2]
D) [L^2 T^-2]
33. The dimensions of velocity are:
A) [M L T^-1]
B) [L T^-1]
C) [M L^-1 T]
D) [L^2 T^-1]
34. Which of the following is a fundamental dimension in the SI system?
A) Force
B) Velocity
C) Mass
D) Energy
35. What is dimensional analysis primarily used for?
A) Calculating precise numerical values
B) Checking the consistency of physical equations
C) Determining the nature of matter
D) Measuring very small distances
36. If V = a^n, the relative error in V is:
A) ΔV/V = n * (Δa/a)
B) ΔV/V = (1/n) * (Δa/a)
C) ΔV/V = n^2 * (Δa/a)
D) ΔV/V = sqrt(n) * (Δa/a)
37. If P = a / b, and the relative errors in a and b are Δa/a and Δb/b, the relative error in P is:
A) ΔP/P = Δa/a - Δb/b
B) ΔP/P = Δa/a + Δb/b
C) ΔP/P = (Δa/a) * (Δb/b)
D) ΔP/P = (Δa/a) / (Δb/b)
38. If z = a * b, and the relative errors in a and b are Δa/a and Δb/b, the relative error in z is:
A) Δz/z = Δa/a - Δb/b
B) Δz/z = Δa/a + Δb/b
C) Δz/z = (Δa/a) * (Δb/b)
D) Δz/z = (Δa/a) / (Δb/b)
39. If y = a - b, and the errors in a and b are Δa and Δb, the error in y is:
A) Δy = Δa + Δb
B) Δy = Δa - Δb
C) Δy = Δa * Δb
D) Δy = Δa / Δb
40. If x = a + b, and the errors in a and b are Δa and Δb, the error in x is:
A) Δx = Δa - Δb
B) Δx = Δa + Δb
C) Δx = Δa * Δb
D) Δx = Δa / Δb
41. In the measurement of length 'l' = 10.0 ± 0.1 cm, what is the percentage error?
A) 1%
B) 0.1%
C) 10%
D) 0.01%
42. If a quantity is raised to a power 'n', the relative error in the result is:
A) n times the relative error of the quantity
B) 1/n times the relative error of the quantity
C) n squared times the relative error of the quantity
D) The square root of n times the relative error of the quantity
43. When dividing two quantities with their relative errors, the relative error in the quotient is:
A) The difference of the relative errors
B) The product of the relative errors
C) The sum of the relative errors
D) The ratio of the relative errors
44. When multiplying two quantities with their relative errors, the relative error in the product is:
A) The difference of the relative errors
B) The product of the relative errors
C) The sum of the relative errors
D) The ratio of the relative errors
45. When subtracting two quantities with their absolute errors, the absolute error in the difference is:
A) The sum of the absolute errors
B) The difference of the absolute errors
C) The product of the absolute errors
D) The ratio of the absolute errors
46. When adding two quantities with their absolute errors, the absolute error in the sum is:
A) The difference of the absolute errors
B) The sum of the absolute errors
C) The product of the absolute errors
D) The ratio of the absolute errors
47. If the absolute error is 0.02 m and the true value is 2.5 m, what is the percentage error?
A) 0.8%
B) 0.08%
C) 8%
D) 2%
48. If the measured value is 10 units and the true value is 12 units, what is the relative error?
A) 1/6
B) 1/5
C) 5/6
D) 6/5
49. If a measurement is 5.0 cm and the true value is 5.1 cm, what is the absolute error?
A) 0.1 cm
B) -0.1 cm
C) 5.0 cm
D) 5.1 cm
50. Percentage error is defined as:
A) Relative Error * 100%
B) Absolute Error / 100%
C) True Value * Relative Error
D) Measured Value * 100%
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