1. Which of the following is a dimensionless constant?
A.
Acceleration due to gravity
B.
Gravitational constant
C.
π
D.
Speed of light
Correct Answer:
π
Explanation:
π is a pure numerical constant and has no dimensions.
2. The numerical value of a dimensionless constant remains unchanged when the system of units is changed. Which of the following is such a constant?
A.
2
B.
5 m
C.
9.8 m/s²
D.
6.67 × 10⁻¹¹ N m²/kg²
Correct Answer:
2
Explanation:
A pure number such as 2 has no dimensions, so its value does not depend on the system of units.
3. Which of the following is dimensionless?
A.
Refractive index
B.
Wavelength
C.
Frequency
D.
Intensity
Correct Answer:
Refractive index
Explanation:
Refractive index is the ratio of the speed of light in vacuum to its speed in a medium, so its dimensions cancel.
4. The coefficient of friction between two surfaces is a dimensionless constant because it is defined as the ratio of:
A.
Work to time
B.
Frictional force to normal force
C.
Distance to time
D.
Mass to volume
Correct Answer:
Frictional force to normal force
Explanation:
Both frictional force and normal force have the dimensions of force, so their ratio has no dimensions.
5. Which of the following is a dimensionless constant commonly used in physics?
A.
Density of water
B.
Relative density
C.
Pressure
D.
Momentum
Correct Answer:
Relative density
Explanation:
Relative density is the ratio of the density of a substance to the density of a reference substance, making it dimensionless.
6. The angle measured in radians is dimensionless because it is the ratio of:
A.
Radius to arc length
B.
Arc length to radius
C.
Area to radius
D.
Diameter to circumference
Correct Answer:
Arc length to radius
Explanation:
Both arc length and radius have the dimension of length, so their ratio, the angle in radians, is dimensionless.
7. Which of the following quantities is a dimensionless constant?
A.
Strain
B.
Stress
C.
Young's modulus
D.
Pressure
Correct Answer:
Strain
Explanation:
Strain is the ratio of change in length to original length, so the dimensions of length cancel.
8. The mathematical constant e is classified as a dimensionless constant because it is:
A.
A length
B.
A force
C.
A pure number
D.
A time interval
Correct Answer:
A pure number
Explanation:
The constant e is a pure numerical value and therefore has no physical dimensions.
9. Which of the following ratios represents a dimensionless constant?
A.
Mass divided by volume
B.
Distance divided by time
C.
Energy divided by time
D.
Circumference divided by diameter
Correct Answer:
Circumference divided by diameter
Explanation:
Circumference and diameter both have the dimension of length, so their ratio π is dimensionless.
10. A dimensionless constant has which of the following dimensional formulas?
A.
[M]
B.
[L T⁻¹]
C.
[M L² T⁻²]
D.
[M⁰ L⁰ T⁰]
Correct Answer:
[M⁰ L⁰ T⁰]
Explanation:
A dimensionless constant has zero powers of mass, length, and time, giving the dimensional formula [M⁰ L⁰ T⁰].
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