physics : class11 Fundamental Physical Dimensions : Dimensions of Physical Quantities : Physical World and Measurement MCQ Questions and Answers
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Fundamental Physical Dimensions
MCQ questions and answers.
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MCQ Questions
1. Which set contains only independent fundamental physical dimensions in the SI system?
A.
[M], [L], [T], [I], [Θ], [N], [J]
B.
[M], [L], [T], [F], [Θ], [N], [J]
C.
[M], [L], [T], [E], [Θ], [N], [J]
D.
[M], [L], [T], [P], [Θ], [N], [J]
Correct Answer:
[M], [L], [T], [I], [Θ], [N], [J]
Explanation:
The seven SI fundamental dimensions are mass [M], length [L], time [T], electric current [I], thermodynamic temperature [Θ], amount of substance [N], and luminous intensity [J]. Force, energy, and power are derived dimensions.
2. A physical quantity has dimensional representation [M^0L^0T^0I^0Θ^0N^0J^0]. Which statement is necessarily correct?
A.
It must be a pure number and have no unit in every system
B.
It is dimensionless, although it may possess a named unit
C.
It must represent an angle only
D.
It must be a fundamental quantity
Correct Answer:
It is dimensionless, although it may possess a named unit
Explanation:
All fundamental exponents being zero means the quantity is dimensionless. Dimensionless quantities can nevertheless have named units, such as the radian or steradian.
3. Which pair consists of two quantities that are dimensionally identical but represent different physical concepts?
A.
Mass and weight
B.
Pressure and energy
C.
Impulse and momentum
D.
Power and force
Correct Answer:
Impulse and momentum
Explanation:
Impulse has dimensions [force × time] = [MLT^-1], which is also the dimensional formula of momentum. Mass and weight, for example, differ because weight has dimensions [MLT^-2].
4. If a new fundamental quantity X is assigned the dimensions [M^aL^bT^c], which condition is required for X to be independent of mass, length, and time?
A.
a + b + c = 1
B.
abc = 1
C.
At least one of a, b, or c must be nonzero
D.
X cannot be independent if its dimensions involve M, L, or T
Correct Answer:
X cannot be independent if its dimensions involve M, L, or T
Explanation:
A quantity whose dimensions can be expressed as powers of existing fundamental dimensions is derived from them. Therefore, a genuinely independent fundamental quantity cannot have dimensions reducible to [M], [L], and [T].
5. Which dimensional expression correctly represents electric charge using fundamental dimensions of mass, length, time, and electric current?
A.
[M^0L^0T^1I^1]
B.
[M^0L^0T^{-1}I^1]
C.
[M^0L^0T^1I^{-1}]
D.
[M^1L^0T^1I^1]
Correct Answer:
[M^0L^0T^1I^1]
Explanation:
Electric charge equals electric current multiplied by time. Hence, its dimensions are [I][T] = [M^0L^0T^1I^1].
6. Which of the following quantities introduces the fundamental dimension of thermodynamic temperature into its dimensional formula?
A.
Heat capacity
B.
Specific heat capacity
C.
Entropy
D.
Coefficient of linear expansion
Correct Answer:
Coefficient of linear expansion
Explanation:
The coefficient of linear expansion is defined as fractional change in length per unit temperature change, so its dimensions are [Θ^-1]. Heat capacity, specific heat capacity, and entropy also involve temperature in more complex derived forms, but the coefficient directly introduces the inverse temperature dimension.
7. Which one of the following is a fundamental SI quantity rather than a quantity derived from other fundamental quantities?
A.
Plane angle
B.
Luminous intensity
C.
Electric charge
D.
Force
Correct Answer:
Luminous intensity
Explanation:
Luminous intensity is one of the seven SI base quantities and has fundamental dimension [J]. Plane angle is dimensionless, while charge and force are derived quantities.
8. The dimensional formula of amount of substance in the SI base-dimension notation is represented by which symbol?
A.
[N]
B.
[A]
C.
[mol]
D.
[n]
Correct Answer:
[N]
Explanation:
In dimensional analysis, the fundamental dimension for amount of substance is denoted by [N]. The unit is mole, but [mol] is a unit symbol rather than the conventional dimensional symbol.
9. A quantity Q has dimensions [M^xL^yT^zI^wΘ^rN^sJ^u]. For Q to have the same dimensions as electric potential, which exponent set is required?
A.
(x, y, z, w, r, s, u) = (1, 2, -3, -1, 0, 0, 0)
B.
(x, y, z, w, r, s, u) = (1, 2, -3, 1, 0, 0, 0)
C.
(x, y, z, w, r, s, u) = (1, 2, -2, -1, 0, 0, 0)
D.
(x, y, z, w, r, s, u) = (1, 1, -3, -1, 0, 0, 0)
Explanation:
Electric potential is work per unit charge. Work has dimensions [ML^2T^-2], and charge has dimensions [IT], so potential has dimensions [ML^2T^-3I^-1]. The remaining fundamental exponents are zero.
10. Which statement most accurately distinguishes a fundamental dimension from a derived dimension?
A.
A fundamental dimension must belong to a scalar quantity, whereas a derived dimension belongs to a vector quantity
B.
A fundamental dimension is selected independently as a base, whereas a derived dimension is expressed as powers of fundamental dimensions
C.
A fundamental dimension has no unit, whereas a derived dimension always has a unit
D.
A fundamental dimension is always dimensionless, whereas a derived dimension is never dimensionless
Correct Answer:
A fundamental dimension is selected independently as a base, whereas a derived dimension is expressed as powers of fundamental dimensions
Explanation:
Fundamental dimensions form an independent basis for describing physical quantities. Derived dimensions, such as those of force or energy, are combinations of the fundamental dimensions.
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