Units And Measurement

01

PYQ 2020

medium

physics ID: mht-cet-

An iron rod is placed parallel to the magnetic field of intensity 2000 . The magnetic flux through the rod is and its cross-sectional area is . The magnetic permeability of the rod in is

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02

PYQ 2020

medium

physics ID: mht-cet-

A wire has a length of 2 m and resistance of . It is connected in series with a resistance of and a cell of e.m.f. 2 V. The potential gradient along the wire will be

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03

PYQ 2020

medium

physics ID: mht-cet-

In the equation, and represent pressure and distance respectively. The dimensions of are

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04

PYQ 2020

medium

physics ID: mht-cet-

A force N acts on a particle in the x-direction. The work done by the force in displacing the particle from to m is

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05

PYQ 2020

medium

physics ID: mht-cet-

Let the physical quantity be . If the percentage error in the measurement of,, and is 2%, 3%, and 4% respectively, then the percentage error in the measurement of is:

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14%

2

7%

3

28%

4

21%

06

PYQ 2020

easy

physics ID: mht-cet-

Find the dimensions of the quantity in the equation, where is the time period, is mass, is length, and is the Young’s modulus.

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07

PYQ 2020

medium

physics ID: mht-cet-

Force where and represent displacement and time respectively. The dimensions of the product are

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08

PYQ 2020

medium

physics ID: mht-cet-

$The errors in the measurement of mass and length of the cube is and respectively. The percentage error in the measurement of density of a cube is$

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Official Solution

Correct Option: (4)

$Step 1: Formula for density. Step 2: Error propagation rule. For a quantity, percentage error is: Step 3: Applying given errors. Step 4: Conclusion. The percentage error in density is .$

09

PYQ 2020

medium

physics ID: mht-cet-

$The dimensions of magnetic intensity are$

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Official Solution

Correct Option: (3)

$Step 1: Definition of magnetic intensity. Magnetic intensity is defined as magnetic field per unit permeability. It can also be expressed as: Step 2: Dimensional formula of magnetic field . Step 3: Dimensional formula of permeability . Step 4: Find dimensions of . Step 5: Conclusion. The dimensions of magnetic intensity are .$

10

PYQ 2020

medium

physics ID: mht-cet-

$Which one of the following combination of constants has dimensions of time? [= constant of gravitation, = Planck's constant, = velocity of light]$

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Official Solution

Correct Option: (1)

$Step 1: Write dimensions of constants. Step 2: Find dimensions of . Step 3: Divide by .} Step 4: Take square root. Step 5: Conclusion. The given combination has the dimensions of time.$

11

PYQ 2020

medium

physics ID: mht-cet-

$In an experiment of the measurement of using simple pendulum, the time period was measured with an accuracy of, while the length was measured with an accuracy of . The percentage accuracy in the value of thus obtained is$

1

$0.7%$

2

$0.3%$

3

$0.9%$

4

$0.1%$

Official Solution

Correct Option: (3)

$Step 1: Using the formula for acceleration due to gravity. The formula for using a pendulum is given by: where is the length and is the time period. Step 2: Calculating the accuracy. The percentage error in is given by the sum of the percentage errors in and, since depends on both. The percentage error in is twice the percentage error in, so: Step 3: Conclusion. The correct answer is (C), 0.9%.$

12

PYQ 2020

medium

physics ID: mht-cet-

$If the dimensions of a physical quantity are given by, then the physical quantity is$

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$velocity if$

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$force if$

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$pressure if$

4

$acceleration if$

Official Solution

Correct Option: (3)

$Step 1: Understanding the dimensions. The dimensional formula is given by . This represents a physical quantity with the dimension of length raised to the power of -1, mass raised to the power of 0 (indicating mass is not involved), and time raised to the power of 1. Step 2: Identifying the correct physical quantity. - For velocity, the dimensions are, which do not match. - For force, the dimensions are, which do not match. - For pressure, the dimensions are, which match the given formula. - For acceleration, the dimensions are, which also do not match. Step 3: Conclusion. The physical quantity corresponding to is pressure. Thus, the correct answer is (C).$

13

PYQ 2020

medium

physics ID: mht-cet-

$If,, and denote energy, mass, angular momentum and constant of gravitation respectively, then the quantity has dimensions of$

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$angle$

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$acceleration$

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$velocity$

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$time$

Official Solution

Correct Option: (1)

$Step 1: Write dimensions of given quantities. Step 2: Substitute dimensions. Step 3: Simplify. All fundamental dimensions cancel out, giving a dimensionless quantity. Step 4: Conclusion. A dimensionless quantity corresponds to an angle.$

14

PYQ 2020

medium

physics ID: mht-cet-

$The maximum error in the measurement of mass and length is 4% and 3% respectively. The error in the measurement of density of a cube will be$

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$9 %$

2

$15 %$

3

$13 %$

4

$6 %$

Official Solution

Correct Option: (3)

$Step 1: Understanding the error propagation. The formula for the density of a cube is: where is the mass and is the length. The error in the density is related to the errors in mass and length. For any function, the maximum error in is: Thus, the total error in the density is the sum of the relative errors in mass and length. The given errors are 4% for mass and 3% for length. Therefore, the error in density is: Step 2: Conclusion. Thus, the correct answer is (C) 13 %.$

15

PYQ 2020

medium

physics ID: mht-cet-

$The SI unit of is (= acceleration due to gravity, = constant of gravitation)$

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Official Solution

Correct Option: (2)

$Step 1: Understanding the formula. The gravitational constant has units of and acceleration due to gravity has units of . Thus, the units of are: Step 2: Conclusion. The correct answer is (B), .$

16

PYQ 2022

easy

physics ID: mht-cet-

$What is the density of water in kgdm -3 if its density in gcm -3 is 0.863?$

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$7.86$

2

$0.863$

3

$8.63$

4

$4.6$

Official Solution

Correct Option: (2)

$Concept: When converting units of density, it's important to understand the relationship between different metric volume and mass units. In this case, we are asked to convert the density of water from grams per cubic centimeter (g/cm³) to kilograms per cubic decimeter (kg/dm³) . Let’s break it down: • 1 gram (g) = 0.001 kilogram (kg) • 1 cubic centimeter (cm³) = 0.001 cubic decimeter (dm³) So, when we convert both the numerator (mass) and the denominator (volume), the factors cancel out: 1 g/cm³ = Step-by-step: • Given density = 0.863 g/cm³ • Using the equivalence above, this directly converts to: \to 0.863 kg/dm³ Conclusion: Since 1 g/cm³ = 1 kg/dm³, the density of water remains numerically the same when converted between these units. Thus, the correct answer is (B) 0.863 .$

17

PYQ 2023

hard

physics ID: mht-cet-

$Find the Current unit conversion from SI to CGS.$

Official Solution

Correct Option: (1)

$To convert current units from the International System of Units (SI) to the Centimeter-Gram-Second (CGS) system, you can use the following conversion factor, which relates the two systems of measurement: In the CGS system, the base unit for measuring electric current is the statampere (stat A), which is different from the Ampere used in the SI system. The relationship between the Ampere and the statampere is such that one Ampere in the SI system is equivalent to statamperes in the CGS system. Therefore, to convert a current value from the SI system to the CGS system, you multiply the value in Amperes by, which means you increase the current by a factor of 1000 . For example, let’s say you have a current of 1 Ampere in the SI system. The conversion to the CGS system would be: If you have 5 Amperes in the SI system, it can be converted to the CGS system as follows: So, 5 Amperes in the SI system is equal to 5000 Amperes in the CGS system. It's important to note that although the CGS system was once used in scientific applications, it has been largely replaced by the more universally adopted SI system . The SI system offers more convenience and consistency in modern physics and engineering, which is why CGS units are no longer as commonly used in practical applications today. However, the conversion factor remains a useful tool when working with older data or in certain fields that still use CGS units.$

18

PYQ 2025

medium

physics ID: mht-cet-

$Which amino acid from following contains as side chain?$

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$Leucine$

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$Alanine$

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$Serine$

4

$Valine$

Official Solution

Correct Option: (2)

$Step 1: Identification Amino acids have a side chain 'R'. - Alanine: - Valine: - Leucine: - Serine: Step 2: Conclusion Alanine is the amino acid with a methyl side chain. Final Answer: (B)$

19

PYQ 2025

medium

physics ID: mht-cet-

$A car travels at a speed of . What is the car's speed in meters per second?$

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Official Solution

Correct Option: (1)

$Step 1: Convert the speed from km/h to m/s To convert a speed from km/h to m/s, use the following conversion factor: Step 2: Apply the conversion Given: - Speed of the car Answer: Therefore, the speed of the car is . So, the correct answer is option (1).$

20

PYQ 2025

medium

physics ID: mht-cet-

$The mass of an object is measured as g and its volume as cm . What is the percentage error in density?$

1

$1.20 %$

2

$0.35 %$

3

$2.04 %$

4

$0.71 %$

Official Solution

Correct Option: (3)

$Given: Mass of the object: Volume of the object: Step 1: Formula for Density The density is given by the formula: where: - is the mass, - is the volume. Step 2: Calculate the Relative Errors The relative error in a calculated quantity is the sum of the relative errors in the measured quantities. So for density, the percentage error is the sum of the percentage errors in mass and volume. The relative error in mass is: The relative error in volume is: Step 3: Total Percentage Error in Density The total percentage error in density is the sum of the percentage errors in mass and volume: Substituting the values: Step 4: Final Answer Rounding the result to two decimal places:$

21

PYQ 2025

medium

physics ID: mht-cet-

$The frequency of fourth overtone of a closed pipe is in unison with the fifth overtone of an open pipe. The ratio of length of closed pipe to that of open pipe is$

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Official Solution

Correct Option: (4)

$Concept: For closed pipe: For open pipe: Step 1: Find frequencies. 4th overtone (closed pipe) â 9th harmonic: 5th overtone (open pipe) â 6th harmonic: Step 2: Equate frequencies. Step 3: Solve ratio. But considering correct overtone relation gives: Step 4: Conclusion.$

22

PYQ 2025

easy

physics ID: mht-cet-

$Mass =, Volume = . What is the percentage error in density?$

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Official Solution

Correct Option: (2)

$The density of an object is given by the formula: Given: - Mass = g - Volume = cmÂ³ The formula for density error is: where: - (uncertainty in mass), -, - (uncertainty in volume), - . Substituting the given values: First, calculate the individual percentage errors: -, - . Now, add the errors: Thus, the percentage error in density is approximately$

High-Yield Trend

Chapter Questions
22 MCQs

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Step 1: Formula for Density

Step 2: Calculate the Relative Errors

Step 3: Total Percentage Error in Density

Step 4: Final Answer

Official Solution

Official Solution

Units And Measurement

High-Yield Trend

Chapter Questions 22 MCQs

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Step 1: Formula for Density

Step 2: Calculate the Relative Errors

Step 3: Total Percentage Error in Density

Step 4: Final Answer

Official Solution

Official Solution

Chapter Questions
22 MCQs