physics : class11 Dimensionless Quantities : Dimensions of Physical Quantities : Physical World and Measurement MCQ Questions and Answers
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Dimensionless Quantities
MCQ questions and answers.
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MCQ Questions
1. Which of the following physical quantities is dimensionless?
A.
Velocity
B.
Force
C.
Strain
D.
Work
Correct Answer:
Strain
Explanation:
Strain is the ratio of change in length to original length. Since both quantities have the same dimensions, their ratio has no dimensions.
2. What are the dimensions of the coefficient of friction?
A.
[M L T^-2]
B.
[M L^-1 T^-2]
C.
[1]
D.
[L T^-1]
Correct Answer:
[1]
Explanation:
The coefficient of friction is the ratio of frictional force to normal force. Since both are forces, the ratio is dimensionless.
3. Which of the following is a dimensionless quantity?
A.
Density
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 water. The dimensions cancel, so it is dimensionless.
4. The dimensional formula of a plane angle is:
A.
[M L T^-2]
B.
[L]
C.
[1]
D.
[L^-1]
Correct Answer:
[1]
Explanation:
A plane angle is defined as the ratio of arc length to radius. Both have the dimension of length, so the angle is dimensionless.
5. Which quantity has no dimensions but may have the unit radian?
A.
Plane angle
B.
Area
C.
Angular velocity
D.
Torque
Correct Answer:
Plane angle
Explanation:
A plane angle is the ratio of arc length to radius, making it dimensionless. Its commonly used unit is the radian.
6. The refractive index of a medium is a:
A.
Dimensionless quantity
B.
Quantity with dimensions [L]
C.
Quantity with dimensions [T]
D.
Quantity with dimensions [M L T^-1]
Correct Answer:
Dimensionless quantity
Explanation:
Refractive index is defined as the ratio of the speed of light in vacuum to its speed in the medium. Both speeds have the same dimensions, so the ratio is dimensionless.
7. What is the dimensional nature of a solid angle?
A.
[L^2]
B.
[L]
C.
[1]
D.
[M L^2 T^-2]
Correct Answer:
[1]
Explanation:
A solid angle is the ratio of an area on a sphere to the square of its radius. Both have dimensions of area, so the solid angle is dimensionless.
8. Which of the following ratios is dimensionless?
A.
Distance divided by time
B.
Mass divided by volume
C.
Work divided by energy
D.
Force divided by area
Correct Answer:
Work divided by energy
Explanation:
Work and energy have the same dimensions. Therefore, their ratio is dimensionless.
9. The dimensional formula of relative permittivity is:
A.
[M L T^-2]
B.
[1]
C.
[M^-1 L^-3 T^4 A^2]
D.
[L T^-1]
Correct Answer:
[1]
Explanation:
Relative permittivity is the ratio of the permittivity of a medium to the permittivity of free space. Since both have identical dimensions, the ratio is dimensionless.
10. Which quantity is dimensionless because it is a ratio of two lengths?
A.
Speed
B.
Acceleration
C.
Strain
D.
Displacement
Correct Answer:
Strain
Explanation:
Strain is the ratio of change in length to the original length. The dimensions of length cancel, leaving a dimensionless quantity.
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