What is the principle of dimensional analysis used for?
a) Determining physical quantities
b) Converting units
c) Checking the correctness of equations
d) Finding numerical values
Which of the following is a basic dimension in dimensional analysis?
a) Velocity
b) Force
c) Length
d) Pressure
What is the dimensional formula of acceleration?
a) [M L T⁻²]
b) [M L T⁻³]
c) [M L² T⁻²]
d) [M L T⁻¹]
Which physical quantity has the dimensional formula [M⁰ L¹ T⁻²]?
a) Force
b) Work
c) Pressure
d) Velocity
In dimensional analysis, what does the letter “M” represent?
a) Mass
b) Length
c) Time
d) Energy
What is the dimensional formula of Planck’s constant (h)?
a) [M L² T⁻¹]
b) [M L³ T⁻²]
c) [M L T⁻²]
d) [M L² T⁻²]
Which of the following is used in the method of dimensional analysis to check the correctness of physical equations?
a) Principle of homogeneity
b) Theorem of compatibility
c) Law of conservation of energy
d) Principle of energy exchange
What is the dimensional formula of force?
a) [M L T⁻²]
b) [M L² T⁻²]
c) [M L T]
d) [M L T⁻¹]
What is the dimensional formula of energy?
a) [M L² T⁻²]
b) [M L³ T⁻²]
c) [M L T⁻¹]
d) [M L² T⁻³]
Which quantity is dimensionless in a dimensional equation?
a) Energy
b) Force
c) Gravitational constant
d) Coefficient of friction
What is the dimensional formula of pressure?
a) [M L T⁻²]
b) [M L⁻¹ T⁻²]
c) [M L² T⁻²]
d) [M L T⁻²]
Which physical quantity can be derived by using dimensional analysis?
a) Gravitational constant
b) Universal gas constant
c) Planck’s constant
d) All of the above
What is the purpose of the Buckingham π theorem in dimensional analysis?
a) To derive the dimensional formula
b) To derive the relationship between variables
c) To simplify equations
d) To convert units
In dimensional analysis, which of the following is not a base dimension?
a) Mass
b) Time
c) Velocity
d) Length
What is the unit of velocity in SI system?
a) [M L² T⁻²]
b) [M L T⁻¹]
c) [M L T]
d) [M T⁻²]
What is the dimensional formula for frequency?
a) [T⁻¹]
b) [M T]
c) [M L T⁻¹]
d) [L T⁻¹]
Which of the following quantities has the dimensional formula [M L² T⁻²]?
a) Work
b) Force
c) Power
d) Pressure
What does the dimensional formula of a physical quantity help to determine?
a) The measurement unit
b) The exact value
c) The relationship with other quantities
d) The symmetry properties
Which of the following is an example of a dimensionless constant in dimensional analysis?
a) Gravitational constant
b) Pi (π)
c) Boltzmann constant
d) Planck’s constant
The dimensional formula of the universal gas constant (R) is:
a) [M L² T⁻² K⁻¹]
b) [M L³ T⁻² K⁻¹]
c) [M L² T⁻²]
d) [M L T⁻² K⁻¹]
Which of the following dimensions are required for a formula to be dimensionally homogeneous?
a) Length and Time
b) Mass and Time
c) Mass, Length, and Time
d) Mass, Time, and Temperature
What is the unit of work in the SI system?
a) Joule
b) Newton
c) Watt
d) Ampere
Which of the following is a dimensionless number in fluid dynamics?
a) Reynolds number
b) Gravitational constant
c) Speed of light
d) Energy
What is the dimensional formula of torque?
a) [M L² T⁻²]
b) [M L T⁻²]
c) [M L T⁻¹]
d) [M L² T⁻³]
The principle of homogeneity in dimensional analysis states that:
a) All dimensions must be in SI units
b) The units of all terms in an equation must be the same
c) The dimensions of a derived formula must match those of the original formula
d) Dimensions of velocity are equal to the square of those of force
What is the dimensional formula for gravitational potential energy?
a) [M L² T⁻²]
b) [M L² T⁻³]
c) [M L T⁻²]
d) [M L³ T⁻²]
The dimensional formula for power is:
a) [M L² T⁻³]
b) [M L² T⁻²]
c) [M L T⁻²]
d) [M T⁻²]
What is the dimensional formula for the universal gravitational constant (G)?
a) [M⁻¹ L³ T⁻²]
b) [M L³ T⁻²]
c) [M L² T⁻²]
d) [M⁻² L³ T⁻²]
Which of the following quantities is measured in watts?
a) Work
b) Energy
c) Power
d) Force
In dimensional analysis, the number of fundamental dimensions in any physical system is:
a) 3
b) 4
c) 5
d) 6
