Errors in measurements and dimensional analysis - One Line Questions
1.
The dimensions of acceleration are: —
[L T^-2]
2.
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: —
[L T^-2]
3.
The dimensions of velocity are: —
[L T^-1]
4.
The dimensions of impulse are: —
[M L T^-1]
5.
The dimensions of force are: —
[M L T^-2]
6.
The dimensions of coefficient of viscosity are: —
[M L^-1 T^-1]
7.
The dimensions of pressure are: —
[M L^-1 T^-2]
8.
The dimensions of density are: —
[M L^-3]
9.
The dimensions of Planck's constant (h) are: —
[M L^2 T^-1]
10.
The dimensions of angular momentum are: —
[M L^2 T^-1]
11.
The dimensions of the universal gas constant (R) are: —
[M L^2 T^-2 K^-1]
12.
The dimensions of energy are: —
[M L^2 T^-2]
13.
The dimensions of surface tension are: —
[M T^-2]
14.
The dimensions of Stefan's constant are: —
[M T^-3 K^-4]
15.
The dimensions of the gravitational constant (G) are: —
[M^-1 L^3 T^-2]
16.
The dimensions of angular velocity are: —
[T^-1]
17.
The dimensions of angular acceleration are: —
[T^-2]
18.
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)? —
±3%
19.
If a measurement is 5.0 cm and the true value is 5.1 cm, what is the absolute error? —
-0.1 cm
20.
A measurement has an error of ±0.5 units. If the measured value is 10.0 units, what is the percentage error? —
5%
21.
If the error in measuring the diameter of a wire is 1%, what is the error in measuring its radius? —
1%
22.
If the absolute error is 0.02 m and the true value is 2.5 m, what is the percentage error? —
0.8%
23.
If the measured value is 10 units and the true value is 12 units, what is the relative error? —
1/6
24.
In the measurement of length 'l' = 10.0 ± 0.1 cm, what is the percentage error? —
1%
25.
If the error in measuring the radius of a circle is 1%, what is the error in measuring its area? —
2%
26.
The error in measuring the side of a cube is 2%. What is the maximum percentage error in its volume? —
6%
27.
If the error in measuring the velocity of a particle is 3%, what is the error in measuring its kinetic energy? —
6%
28.
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: —
11%
29.
Which of the following represents the relative error? —
Absolute Error / True Value
30.
Which of the following is a derived unit? —
Watt
31.
What is dimensional analysis primarily used for? —
Checking the consistency of physical equations
32.
Dimensional analysis cannot be used to: —
Determine the value of dimensionless constants
33.
The principle of homogeneity of dimensions states that: —
Dimensions of each term in an equation must be the same
34.
Which of the following is a fundamental dimension in the SI system? —
Mass
35.
Which of the following is NOT a fundamental unit in the SI system? —
Newton
36.
If a quantity is raised to a power 'n', the relative error in the result is: —
n times the relative error of the quantity
37.
If a quantity 'x' depends on 'y' and 'z' as x = y^n * z^m, the relative error in x is given by: —
n(Δy/y) + m(Δz/z)
38.
The dimensions of work done are the same as: —
Energy
39.
Percentage error is defined as: —
Relative Error * 100%
40.
Which of the following is a dimensionless quantity? —
Strain
41.
When adding two quantities with their absolute errors, the absolute error in the sum is: —
The sum of the absolute errors
42.
When multiplying two quantities with their relative errors, the relative error in the product is: —
The sum of the relative errors
43.
When dividing two quantities with their relative errors, the relative error in the quotient is: —
The sum of the relative errors
44.
What is the absolute error in a measurement? —
The difference between the true value and the measured value
45.
When subtracting two quantities with their absolute errors, the absolute error in the difference is: —
The sum of the absolute errors
46.
If a quantity 'Q' is measured as x ± Δx, then Δx represents: —
The absolute error in Q
47.
Which of the following is a unit of energy? —
Joule
48.
If P = a / b, and the relative errors in a and b are Δa/a and Δb/b, the relative error in P is: —
ΔP/P = Δa/a + Δb/b
49.
If V = a^n, the relative error in V is: —
ΔV/V = n * (Δa/a)
50.
If x = a + b, and the errors in a and b are Δa and Δb, the error in x is: —
Δx = Δa + Δb