physics : class11 Limitations of Dimensional Analysis : Dimensions of Physical Quantities : Physical World and Measurement MCQ Questions and Answers
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Limitations of Dimensional Analysis
MCQ questions and answers.
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MCQ Questions
1. What can dimensional analysis generally not determine in a physical formula?
A.
The dimensions of the quantities
B.
The numerical value of a dimensionless constant
C.
Whether units are consistent
D.
The dimensions of the result
Correct Answer:
The numerical value of a dimensionless constant
Explanation:
Dimensional analysis cannot determine dimensionless numerical constants such as 2, pi, or 1/2.
2. Which limitation of dimensional analysis prevents it from finding whether a formula contains a plus or minus sign?
A.
It cannot identify the nature of the quantities
B.
It cannot determine the units of length
C.
It cannot check the dimensions of a quantity
D.
It cannot measure physical quantities
Correct Answer:
It cannot identify the nature of the quantities
Explanation:
Dimensional analysis checks dimensional consistency but cannot determine the mathematical operation, such as whether terms should be added or subtracted.
3. Dimensional analysis cannot distinguish between which pair of quantities?
A.
Speed and acceleration
B.
Force and energy
C.
Work and torque
D.
Mass and density
Correct Answer:
Work and torque
Explanation:
Work and torque have the same dimensions, although they represent different physical quantities. Thus, dimensional analysis cannot distinguish between them.
4. A dimensionally correct equation may still be physically incorrect because dimensional analysis cannot determine the:
A.
Dimensions of mass
B.
Numerical coefficients in the equation
C.
Dimensions of time
D.
Units used for measurement
Correct Answer:
Numerical coefficients in the equation
Explanation:
An equation can have consistent dimensions while containing an incorrect numerical factor, which dimensional analysis cannot detect.
5. Which type of function cannot usually be obtained using dimensional analysis alone?
A.
A simple product of powers
B.
A ratio of quantities
C.
A trigonometric function
D.
A quantity with known dimensions
Correct Answer:
A trigonometric function
Explanation:
Dimensional analysis cannot derive the exact form of functions such as sine, cosine, or exponential functions.
6. Why can dimensional analysis not derive the exact equation for the period of a pendulum?
A.
It cannot identify the relevant physical quantities
B.
It cannot determine the numerical constant in the equation
C.
It cannot measure the length of the pendulum
D.
It cannot assign dimensions to time
Correct Answer:
It cannot determine the numerical constant in the equation
Explanation:
Dimensional analysis can suggest that the period depends on length and gravitational acceleration, but it cannot determine the numerical factor such as 2 pi.
7. If two quantities have identical dimensions, dimensional analysis alone cannot determine their:
A.
Units
B.
Numerical values
C.
Physical meanings
D.
Dimensions
Correct Answer:
Physical meanings
Explanation:
Different physical quantities may have the same dimensions, so dimensional analysis cannot identify their distinct physical meanings.
8. Which statement shows a limitation of dimensional analysis?
A.
It can test dimensional consistency
B.
It can convert units from one system to another
C.
It can prove that a dimensionally correct equation is physically true
D.
It can find dimensions of derived quantities
Correct Answer:
It can prove that a dimensionally correct equation is physically true
Explanation:
Dimensional consistency is necessary but not sufficient for correctness. A dimensionally correct equation may still be physically wrong.
9. Dimensional analysis is unable to determine the number of independent terms in an equation when the terms have:
A.
Different dimensions
B.
The same dimensions
C.
No units
D.
Only mass dimensions
Correct Answer:
The same dimensions
Explanation:
When several terms have the same dimensions, dimensional analysis alone cannot determine which terms should appear in the equation.
10. Which quantity cannot be determined from dimensional analysis if it is dimensionless?
A.
The dimensions of velocity
B.
The dimensions of force
C.
A numerical constant
D.
The dimensions of energy
Correct Answer:
A numerical constant
Explanation:
Dimensionless constants have no dimensions, so dimensional analysis cannot determine their numerical values.
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