Q. If the length of a side of a cube is doubled, how does its volume change?
A.
Increases by 2 times
B.
Increases by 4 times
C.
Increases by 8 times
D.
Remains the same
Show solution
Solution
The volume of a cube is given by V = a³. If the side length a is doubled, the new volume is (2a)³ = 8a³, which is 8 times the original volume.
Correct Answer:
C
— Increases by 8 times
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Q. If the length of a side of a cube is doubled, how does the volume change?
A.
Increases by 2 times
B.
Increases by 4 times
C.
Increases by 8 times
D.
Remains the same
Show solution
Solution
Volume of a cube is given by V = a³. If a is doubled, V becomes (2a)³ = 8a³, hence volume increases by 8 times.
Correct Answer:
C
— Increases by 8 times
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Q. If the length of an object is doubled, what happens to its area?
A.
It remains the same
B.
It doubles
C.
It triples
D.
It quadruples
Show solution
Solution
If the length is doubled, the area increases by a factor of four (A = length²).
Correct Answer:
D
— It quadruples
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Q. If the length of an object is doubled, what happens to its volume?
A.
It remains the same
B.
It doubles
C.
It triples
D.
It increases by a factor of eight
Show solution
Solution
If the length is doubled, the volume increases by a factor of 2^3 = 8, since volume is proportional to the cube of the length.
Correct Answer:
D
— It increases by a factor of eight
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Q. The dimensional formula for work is:
A.
[M^1 L^2 T^-2]
B.
[M^1 L^1 T^-1]
C.
[M^0 L^2 T^-1]
D.
[M^1 L^0 T^0]
Show solution
Solution
The dimensional formula for work is [M^1 L^2 T^-2].
Correct Answer:
A
— [M^1 L^2 T^-2]
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Q. The unit of electric charge in SI is?
A.
Coulomb
B.
Ampere
C.
Volt
D.
Ohm
Show solution
Solution
The SI unit of electric charge is Coulomb (C).
Correct Answer:
A
— Coulomb
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Q. The unit of energy in the SI system is:
A.
Joule
B.
Calorie
C.
Watt
D.
Newton
Show solution
Solution
The SI unit of energy is Joule (J).
Correct Answer:
A
— Joule
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Q. What are the dimensions of pressure?
A.
ML^-1T^-2
B.
ML^2T^-2
C.
ML^2T^-1
D.
M^0L^0T^0
Show solution
Solution
Pressure is defined as force per unit area. The dimensions of force are ML^1T^-2, and area is L^2, thus pressure has dimensions ML^-1T^-2.
Correct Answer:
A
— ML^-1T^-2
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Q. What is the dimension of electric charge?
A.
[M^1 L^2 T^-3 I^1]
B.
[M^0 L^0 T^0 I^1]
C.
[M^1 L^1 T^-2 I^1]
D.
[M^0 L^1 T^-1 I^1]
Show solution
Solution
The dimension of electric charge is [M^1 L^2 T^-3 I^1].
Correct Answer:
A
— [M^1 L^2 T^-3 I^1]
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Q. What is the dimension of frequency?
A.
M^0L^0T^-1
B.
M^1L^0T^-1
C.
M^0L^1T^-1
D.
M^0L^0T^0
Show solution
Solution
Frequency is defined as the number of cycles per unit time, thus its dimension is [M^0L^0T^-1].
Correct Answer:
A
— M^0L^0T^-1
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Q. What is the dimension of the gravitational constant G?
A.
M^-1L^3T^-2
B.
M^1L^3T^-2
C.
M^1L^2T^-2
D.
M^0L^0T^0
Show solution
Solution
The gravitational constant G has dimensions of [M^-1L^3T^-2] as it relates mass, distance, and time in the law of gravitation.
Correct Answer:
A
— M^-1L^3T^-2
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Q. What is the dimensional formula for acceleration?
A.
[M^0 L^1 T^-2]
B.
[M^0 L^0 T^-2]
C.
[M^1 L^1 T^-2]
D.
[M^1 L^0 T^-2]
Show solution
Solution
The dimensional formula for acceleration is [M^0 L^1 T^-2], as it is defined as the change in velocity per unit time.
Correct Answer:
A
— [M^0 L^1 T^-2]
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Q. What is the dimensional formula for electric charge?
A.
[M^1 L^2 T^-3 I^-1]
B.
[M^0 L^0 T^1 I^1]
C.
[M^0 L^1 T^-2 I^1]
D.
[M^1 L^1 T^-2 I^-1]
Show solution
Solution
The dimensional formula for electric charge is [M^1 L^2 T^-3 I^-1], derived from the definition of current (I = Q/t).
Correct Answer:
A
— [M^1 L^2 T^-3 I^-1]
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Q. What is the dimensional formula for frequency?
A.
[M^0 L^0 T^-1]
B.
[M^1 L^0 T^-1]
C.
[M^0 L^1 T^0]
D.
[M^0 L^0 T^1]
Show solution
Solution
The dimensional formula for frequency is [M^0 L^0 T^-1], as it is defined as the number of cycles per unit time.
Correct Answer:
A
— [M^0 L^0 T^-1]
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Q. What is the dimensional formula for velocity?
A.
MLT⁻¹
B.
ML²T⁻²
C.
M⁰L⁰T⁻¹
D.
M⁰L¹T⁻²
Show solution
Solution
Velocity is defined as displacement per unit time, which gives the dimensional formula of [MLT⁻¹].
Correct Answer:
A
— MLT⁻¹
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Q. What is the dimensional formula for work?
A.
[M^1 L^2 T^-2]
B.
[M^1 L^1 T^-1]
C.
[M^0 L^2 T^-2]
D.
[M^1 L^0 T^-2]
Show solution
Solution
Work has the dimensional formula [M^1 L^2 T^-2].
Correct Answer:
A
— [M^1 L^2 T^-2]
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Q. What is the relationship between Joules and Newton-meters?
A.
They are equal
B.
Joule is greater
C.
Newton-meter is greater
D.
They are unrelated
Show solution
Solution
1 Joule is defined as 1 Newton-meter, so they are equal.
Correct Answer:
A
— They are equal
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Q. What is the relationship between mass and weight?
A.
Weight = Mass × Acceleration due to gravity
B.
Weight = Mass / Acceleration due to gravity
C.
Weight = Mass + Acceleration due to gravity
D.
Weight = Mass - Acceleration due to gravity
Show solution
Solution
Weight is defined as the force due to gravity acting on a mass, given by the formula Weight = Mass × g (where g is the acceleration due to gravity).
Correct Answer:
A
— Weight = Mass × Acceleration due to gravity
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Q. What is the relationship between the units of energy and work?
A.
They are the same
B.
Energy is greater than work
C.
Work is greater than energy
D.
They are different
Show solution
Solution
Energy and work are measured in the same unit, which is Joules (J).
Correct Answer:
A
— They are the same
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Q. What is the relationship between the units of work and energy?
A.
They are the same
B.
Work is a subset of energy
C.
Energy is a subset of work
D.
They are unrelated
Show solution
Solution
Work and energy are measured in the same unit, which is Joules (J) in the SI system.
Correct Answer:
A
— They are the same
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Q. What is the unit of pressure in the SI system?
A.
Pascal
B.
Bar
C.
Torr
D.
Atmosphere
Show solution
Solution
The SI unit of pressure is Pascal (Pa), defined as one newton per square meter (N/m²).
Correct Answer:
A
— Pascal
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Q. Which of the following is a unit of energy?
A.
Joule
B.
Newton
C.
Watt
D.
Pascal
Show solution
Solution
Joule is the unit of energy in the SI system, defined as the work done when a force of one newton displaces an object by one meter.
Correct Answer:
A
— Joule
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Q. Which of the following is NOT a base unit in the SI system?
A.
Meter
B.
Kilogram
C.
Second
D.
Liter
Show solution
Solution
Liter is not a base unit; it is a derived unit for volume, while meter, kilogram, and second are base units.
Correct Answer:
D
— Liter
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Q. Which of the following is not a fundamental unit?
A.
Meter
B.
Kilogram
C.
Second
D.
Joule
Show solution
Solution
Joule is not a fundamental unit; it is a derived unit.
Correct Answer:
D
— Joule
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Q. Which of the following is the correct dimensional formula for electric charge?
A.
[M^1 L^2 T^-3 A^-1]
B.
[M^0 L^0 T^0 A^1]
C.
[M^0 L^1 T^-2 A^1]
D.
[M^1 L^1 T^-2 A^-1]
Show solution
Solution
The dimensional formula for electric charge is [M^1 L^2 T^-3 A^-1], derived from the definition of current.
Correct Answer:
A
— [M^1 L^2 T^-3 A^-1]
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Q. Which of the following is the correct unit for measuring electric charge?
A.
Coulomb
B.
Ampere
C.
Volt
D.
Ohm
Show solution
Solution
The SI unit for electric charge is Coulomb (C).
Correct Answer:
A
— Coulomb
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Q. Which of the following is the correct unit for measuring energy?
A.
Joule
B.
Newton
C.
Watt
D.
Pascal
Show solution
Solution
The correct unit for measuring energy is Joule (J).
Correct Answer:
A
— Joule
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Q. Which of the following quantities has the dimension of energy?
A.
Force
B.
Work
C.
Power
D.
Pressure
Show solution
Solution
Work is defined as force times distance, and its dimensions are ML^2T^-2, which are the same as energy.
Correct Answer:
B
— Work
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Q. Which of the following quantities has the dimension of [M^0 L^0 T^-1]?
A.
Velocity
B.
Acceleration
C.
Frequency
D.
Force
Show solution
Solution
Frequency has the dimension of [M^0 L^0 T^-1] as it is defined as the number of cycles per unit time.
Correct Answer:
C
— Frequency
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Q. Which of the following quantities has the dimension of [M^0 L^0 T^0]?
A.
Mass
B.
Time
C.
Length
D.
Angle
Show solution
Solution
Angle is a dimensionless quantity and has the dimension of [M^0 L^0 T^0].
Correct Answer:
D
— Angle
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Showing 1 to 30 of 40 (2 Pages)
Units & Dimensions MCQ & Objective Questions
Understanding "Units & Dimensions" is crucial for students preparing for exams. This topic lays the foundation for various concepts in physics and mathematics, making it essential for scoring well. Practicing MCQs and objective questions not only enhances your grasp of the subject but also boosts your confidence in tackling important questions during exams.
What You Will Practise Here
Fundamental and derived units in the SI system
Dimensional analysis and its applications
Conversion of units and dimensional formulas
Key concepts of length, mass, time, and their interrelations
Common physical quantities and their dimensions
Applications of dimensional analysis in solving problems
Important formulas related to units and dimensions
Exam Relevance
The topic of "Units & Dimensions" frequently appears in CBSE, State Boards, NEET, and JEE examinations. Students can expect questions that test their understanding of unit conversions, dimensional formulas, and the application of dimensional analysis. Common question patterns include direct MCQs, numerical problems, and conceptual questions that require a clear understanding of the subject.
Common Mistakes Students Make
Confusing fundamental units with derived units
Incorrectly applying dimensional formulas in calculations
Overlooking unit conversions in problem-solving
Misinterpreting the significance of dimensions in physical equations
Neglecting to check the dimensional consistency of equations
FAQs
Question: What are the basic units in the SI system?Answer: The basic units in the SI system include meter (m) for length, kilogram (kg) for mass, and second (s) for time.
Question: How can dimensional analysis help in solving physics problems?Answer: Dimensional analysis helps verify the correctness of equations and can be used to derive relationships between physical quantities.
Now is the time to enhance your understanding of "Units & Dimensions"! Dive into our practice MCQs and test your knowledge to excel in your exams. Remember, consistent practice is the key to success!
