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UNITS AND MEASUREMENT in 1 Shot | FULL Chapter Coverage (Concepts + PYQs) | Class-11th Physics

NCERT Wallah・2 minutes read

Physical quantities are the basis for the laws of physics and Constants play a crucial role in maintaining consistency. The text covers various topics ranging from fundamental quantities to error analysis in measurements.

Insights

  • Constants provide consistency in physical quantities, ensuring no change in values.
  • The SI system and MKS system are crucial for measuring physical quantities accurately.
  • Solid angles, represented by Omega, play a significant role in physics calculations.
  • The Chandrasekhar Limit equates the mass of the sun, highlighting a massive unit of mass.
  • Dimension formulas are essential for understanding and calculating physical quantities accurately.
  • The concept of significant figures is crucial for precision in measurements and calculations.
  • Error analysis in measurements involves identifying and categorizing different types of errors to ensure accuracy in results.

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Recent questions

  • What is the significance of dimensional formulas in physics?

    Dimensional formulas in physics play a crucial role in converting physical quantities between different units, ensuring the correctness of physical equations, and deriving relationships among various physical quantities. These formulas represent the powers to which fundamental quantities like mass, length, and time must be raised to fully describe a physical quantity. By utilizing dimensional analysis, physicists can verify the consistency of equations, identify errors, and establish connections between different variables. Understanding dimensional formulas is essential for accurate calculations and interpretations in the field of physics.

  • How is the concept of precision defined in measurements?

    Precision in measurements refers to the degree of exactness or refinement in determining a value, emphasizing the closeness of multiple measurements to each other. It is characterized by the number of digits after the decimal point, with more decimal places indicating higher precision. Precision plays a vital role in scientific experiments and calculations, as it reflects the reliability and consistency of the obtained results. Instruments with smaller least counts or more decimal points provide greater precision in measurements, enabling researchers to obtain accurate and detailed data for analysis and interpretation.

  • What are the different types of errors in measurements?

    Errors in measurements can be categorized into various types, including constant, systematic, personal, and random errors. Constant errors result from a consistent mistake in measurement, affecting all readings uniformly. Systematic errors arise from faults in experimental setup or calibration, leading to inaccuracies in measurements. Personal errors occur due to observer bias or subjective judgment, influencing the recorded values. Random errors are unpredictable fluctuations in measurements caused by external factors or environmental conditions. Understanding and identifying these error types are essential for improving the accuracy and reliability of experimental data in scientific research.

  • How are significant figures utilized in scientific calculations?

    Significant figures are crucial in scientific calculations as they indicate the precision and reliability of measured values. The number of significant figures in a measurement is determined by the number of digits present, with zeros to the right of a decimal point being considered significant. When performing arithmetic operations, attention to significant figures is necessary to ensure the accuracy of the final result. Multiplication and division require the result to have the same number of significant figures as the factor with the least, while addition and subtraction focus on the minimum number of decimal places. Rounding off numbers based on significant figures is essential for maintaining the appropriate level of precision in scientific computations.

  • How is the concept of elasticity explained in physics?

    Elasticity in physics is governed by Hooke's Law, which states that stress is directly proportional to strain within the elastic limit of a material. Stress represents the force applied per unit area, while strain denotes the deformation or change in shape of the material. The modulus of elasticity quantifies the material's ability to return to its original shape after deformation, with higher values indicating greater elasticity. Understanding elasticity is crucial for predicting the behavior of materials under different conditions, analyzing mechanical properties, and designing structures that can withstand external forces. Hooke's Law serves as a fundamental principle in studying the elasticity of materials and their responses to applied forces.

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Summary

00:00

"Physics: Constants, Units, Formulas, Success"

  • Physical quantities are the basis for the laws of physics and are measurable entities.
  • Constants indicate no change in a physical quantity, providing clarity and consistency.
  • MKS system and SI system are terms used to describe units of measurement.
  • Solid angles are represented by the symbol Omega.
  • The mass of the sun is equivalent to the Chandrasekhar limit.
  • Limits b and c can be determined by selecting them directly.
  • Dimension formulas are crucial in physics calculations.
  • Multiplying a negative number by another negative number results in a positive number.
  • The formula for equivalent resistance in parallel circuits is essential.
  • Motivation and hard work are emphasized for success in physics studies.

15:37

"Measuring Physical Quantities in Science"

  • Temperature is the degree of hotness or coldness of an object, measured to determine its heat or coldness.
  • Current rate is the flow of electric charge, with the battery rate of flow of charge measured in Coulomb seconds, known as amperes.
  • Luminous intensity is the amount of light energy incident per unit area, measured in candela, a fundamental quantity.
  • Mole concept in chemistry represents the amount of substance, calculated by dividing the mass of a substance by its molar mass.
  • Fundamental quantities in physics are independent physical quantities like mass, length, and time, treated as base units.
  • Density is calculated as mass divided by volume, consisting of fundamental quantities and representing the quantity of a substance.
  • Deriving new quantities involves combining fundamental quantities, such as length and breadth to calculate area and volume.
  • Systems of units like MKS, CGS, and FPS are used to measure quantities like length, mass, and time in different units.
  • The SI system, or International System of Units, measures quantities like length in meters, mass in kilograms, and time in seconds.
  • Supplementary quantities like plane angle and solid angle supplement fundamental quantities, with plane angle measured in radians and solid angle representing the angle at the center of a sphere.

34:33

Units and Measurements in Physics

  • Solid angle is defined as the angle subtended by a part of a sphere's surface area at the center of the sphere.
  • The formula for solid angle is surface area divided by the square of the radius of the sphere.
  • The unit of solid angle is steradian, abbreviated as "sr."
  • Fermi is a unit equal to 10^-15 meters, while an angstrom is equal to 10^-10 meters.
  • A micron is equivalent to 10^-6 meters.
  • A light year is the distance traveled by light in a vacuum in one year, approximately equal to 9.46 * 10^15 meters.
  • An astronomical unit is the average distance between the Earth and the Sun, about 1.49 * 10^11 meters.
  • A ton is equal to 1000 kg, while a pound is approximately 453.6 grams.
  • The Chandrasekhar Limit is 1.4 times the mass of the Sun, representing a large unit of mass.
  • Dimension is the power to which fundamental quantities must be raised to represent a physical quantity completely.

51:42

Units and Formulas in Physics Dimensions

  • Candela is the unit of temperature, represented by k in square brackets or theta in square brackets.
  • Luminous intensity is represented by CD in brackets.
  • The amount of substance is represented by square brackets.
  • The dimension formula for fundamental quantities includes m for length, t for time, and k for current and temperature.
  • The dimension formula for volume is l3.
  • The formula for volume is l*l*l.
  • The dimension formula for force is ml-2161.
  • The formula for torque is ml2 t-2.
  • The dimension formula for impulse is m AT-1.
  • Stress is the resistive force divided by the area of the cross-section.

01:08:32

Forces, stress, and dimensions in physics.

  • In equilibrium, forces and furies are equal, leading to the formula f/a, where pressure and stress are distinct concepts.
  • Pressure is perpendicular to the surface area, while furrows should be perpendicular to tension.
  • Stress results in a change in length, denoted as strain, with the formula delta A divided by original length.
  • Strain is dimensionless, denoted as m0 l0 t0, indicating no dimensions due to length changes.
  • Elasticity is governed by Hooke's Law, stating stress is proportional to strain, with stress equal to the modulus of elasticity times strain.
  • Surface tension is the force per unit length on a liquid's surface, with a dimension formula of mt-2.
  • Surface energy is the extra energy on the top layer of liquid molecules compared to inner molecules, with a dimension formula similar to surface tension.
  • Viscosity is the resistance to flow in a liquid, with a dimension formula of ml-1 t-1.
  • Plane angle is dimensionless, while angular velocity is the rate of change of angular displacement, with a dimension formula of t-1.
  • Angular acceleration is the change in angular velocity over time, with a dimension formula of t-2, while moment of inertia has a dimension formula of ml2.

01:23:34

Physical Dimension Formulas for Key Concepts

  • Angular Momentum's dimension formula is ml^2 t^-1, also known as Moment of Momentum.
  • Specific heat is responsible for temperature changes or state changes in an object when heat is applied.
  • The formula for heat given to an object is q = mcΔt, where q is the heat, m is the mass, c is the specific heat, and Δt is the change in temperature.
  • Latent heat formula is q = ma, where a change of state occurs in the object without a change in temperature.
  • Universal Gas Constant is crucial for ideal gases and is used to understand gas properties.
  • Ideal Gas Constant is essential for understanding the behavior of gases and their interactions.
  • The dimensional formula for pressure is ml^-1 t^-2, while for volume it is l^3.
  • Electric potential's dimension formula is ml^2 t^-2.
  • The dimension formula for charge is ml^2 t^-3.
  • Dimension formulas are used to convert physical quantities between different units, check the correctness of physical equations, and derive relationships among various physical quantities.

01:38:11

"Physics and Chemistry Exam Success Tips"

  • Physics is a crucial subject for ranking in exams.
  • Chemistry is often chosen due to its perceived ease.
  • Many students find Chemistry to be manageable.
  • Regular practice is essential for improvement in Physics.
  • Daily practice of 15 Physics numericals is recommended.
  • The SL Arora book is a valuable resource for Physics practice.
  • Understanding concepts is emphasized over memorization.
  • Checking the correctness of equations involves dimensional analysis.
  • Only quantities of the same type can be added or subtracted.
  • Deriving relationships between physical quantities requires dimensional analysis.

01:52:16

Centripetal Force Formula and Proportional Constant

  • The value of 'a' is equal to 1 to the power of 'l'.
  • 'b' + 'c' is equal to the power of 'l'.
  • The power of 'l' is 1, and the power of 't' is -b.
  • The power of 't' is -2, making the value of 'b' equal to 2.
  • Equation one is derived from three equations, equation two is considered, and equation three is believed to be the end value of 3 from equations two and three.
  • By putting 'beta 2' in, '2Pc' equals 1, leading to the value of 'C' being 1.
  • The formula for centripetal force is derived as 'k' times the power of mass.
  • The formula for centripetal force is k times mv1/r.
  • The drawback of the method is the inability to find the value of the proportional constant 'k'.
  • The concept of centripetal force is explained in the context of objects in circular motion, with the force always directed towards the center.

02:05:53

"Equation Variables Comparison for Pendulum Time Period"

  • The text discusses the relationship between various variables in a mathematical equation.
  • It emphasizes the importance of comparing both sides of an equation to determine values.
  • The text explains the process of finding the values of variables like a, b, and c through comparison.
  • It highlights the practical application of the derived formula in determining the time period of a simple pendulum.
  • The text provides a step-by-step guide on how to calculate the time period of a simple pendulum practically.
  • It mentions the value of the constant k as 2 for a simple pendulum.
  • The text offers a mnemonic device to remember the formula for the time period of a simple pendulum.
  • It delves into the frequency of a vibrating string and the factors affecting it.
  • The text explores the dimension formula of force based on density, acceleration due to gravity, and frequency.
  • It concludes by presenting a concept-based question on finding the dimension of force in terms of density, acceleration, and frequency.

02:21:02

Equations Solve for Variables in Physics Formula

  • Equation 1 results in -2.
  • Equation 2 is introduced.
  • Equation 3 reveals the value of a.
  • The value of b is determined from the equations.
  • Equation 2 shows -3 times a plus b equals 1, leading to b being 4.
  • The value of b is calculated.
  • Equation 3 presents the value of b as 4.
  • The value of c is derived from the equations.
  • The dimension formula is discussed, focusing on force.
  • The formula for force is determined based on fundamental quantities.

02:36:11

Significant Figures and Rounding in Calculations

  • Significant figures are crucial in calculations, with zeros to the right of a decimal point being significant.
  • The number of significant figures is determined by the number of digits in a measurement, such as 161 pages having three significant figures.
  • Centimeters and days can also contribute to significant figures in measurements.
  • Rounding off numbers involves considering the digit to be rounded and the preceding digit, with values greater than five leading to rounding up.
  • In rounding off, if the digit to be removed is five, the preceding digit determines whether to round up or not.
  • Rounding off numbers like 14.35 involves removing the digit itself, with specific rules for odd and even numbers.
  • The process of rounding off numbers is detailed, emphasizing the importance of the preceding digit in determining the final value.
  • Arithmetic operations with significant figures require attention to decimal places, ensuring the result aligns with the factor with the least number of decimal places.
  • Multiplication and division with significant figures necessitate the same number of significant figures in the product as the factor with the least significant figures.
  • Adding and subtracting numbers with decimals involves considering the minimum number of decimal places in the calculation to determine the final result.

02:50:25

Volume and Precision in M.Tech Studies

  • M.Tech studies were discovered and a subcategory was incorrectly identified.
  • Decimal points with three digits were discussed, with an example of 47 being rounded.
  • The calculation of the surface area and volume of a cube was explained, emphasizing the six faces of a cube.
  • The process of multiplying to find the volume of a cube was detailed, resulting in 3112.99254.
  • Significant figures in multiplication were highlighted, with the final answer rounded off to 3113.
  • The comparison of significant figures in the answer was discussed, leading to the final result of 3113.
  • The volume of a cube was calculated by cubing the side length, resulting in 37371.47544.
  • The significance of significant figures in division was explained, leading to the density of a substance being 4.8 grams per centimeter cubed.
  • Error analysis in measurements was introduced, distinguishing between mistakes and sins in measurement.
  • The concepts of accuracy and precision in measurements were elaborated upon, emphasizing the closeness to the true value and the resolution of the measurement, respectively.

03:05:44

"Precision in Measurements: Decimal Points and Errors"

  • Precision in measurements is crucial, with more decimal points indicating higher precision.
  • The use of instruments like screw gauges can provide more accurate results.
  • Majoring in measurements with different decimal points can affect precision.
  • In physics, the last digit in a measurement is considered the doubtful digit.
  • Precision is determined by the number of digits after the decimal point.
  • The least count of an instrument affects its precision, with more counts indicating higher precision.
  • Errors in measurements can be categorized into constant, systematic, personal, and random errors.
  • Instrumental errors can arise from faulty calibration or imperfections in experimental techniques.
  • Personal errors occur when the observer is biased, leading to inaccurate measurements.
  • Calculating the mean value of multiple measurements involves adding all values and dividing by the number of measurements.

03:21:46

Error Analysis and Propagation in Measurements

  • The average value of 2.63, 2.56, 2.42, 2.71, and 2.80 is calculated to be 13.12 divided by 5, resulting in a son value of 2.62.
  • Absolute errors in each measurement are determined by subtracting the true value from the measured value, with examples provided for each measurement.
  • Mean Absolute Error is calculated by summing the absolute errors and dividing by 5, considering only positive values.
  • Relative error is found by dividing the absolute error by the true value, resulting in a fractional error without units.
  • Percentage error is calculated by multiplying the fractional error by 100, yielding a percentage value.
  • The result is expressed in proper form as the true value plus or minus the absolute error.
  • The propagation of error in the sum of two quantities is discussed, emphasizing the algebraic sum of absolute errors in x and y.
  • Maximum allowed error in the sum of quantities is equal to the sum of absolute errors in the individual quantities.
  • The same principles are applied to the difference in quantities, with the absolute error in z being the sum of absolute errors in x and y.
  • Error propagation in the product of two quantities is explained, with the fraction error in z equal to the sum of fraction errors in x and y.

03:39:40

Mathematical Formulas and Error Calculations in Physics

  • Factorial is a simple concept where, for example, 5 factorial is 5 * 4 * 3 * 2 * 1.
  • The formula 1 + x to the power of n can be expanded using the formula 1 + nx + n(n-1)x^2/2! + n(n-1)(n-2)x^3/3! and so on.
  • In physics, if the value of x is much less than 1, terms with high powers of x become negligible.
  • For 1 - x to the power -1, if x is much smaller than 1, the expansion simplifies to 1 + x.
  • Error considerations in physics involve formulas like z + Δz/z = 1 + Δx/x and z + Δz/z = 1 + Δy/y.
  • Maximum allowed error in physics is calculated as Δz/z = Δx/x + Δy/y.
  • In series circuits, the equivalent resistance is found by adding the resistances together.
  • To find the sum of two masses, simply add the masses together along with their errors.
  • Percentage error in resistance can be calculated using the formula Δr/r = Δv/v - Δi/i.
  • For errors in measurements of a cube's side and mass, the maximum permissible force can be determined using error calculations.

03:56:17

Error Analysis in Physics Experiments

  • The error in the variable Delta r / r * Ba 100 is three times the percentage error in radius, resulting in a 6% error in volume.
  • When measuring mass and speed at R2 and 3, the maximum error in estimating kinetic energy observed by measuring mass and speed is calculated using the formula 1/2 mv2, leading to an error of delta m/m LT 100 times delta v/v LT.
  • The percentage error in the volume of a rectangular block of wood is determined by calculating delta v/v as delta l/l*100 + delta b/b*100 + delta h/h*100, with specific values provided for delta A, delta B, delta H, A, B, and H.
  • The accuracy in determining the acceleration due to gravity (g) is calculated by considering the measured value of l, the time period of the pendulum, and the resolution of the wristwatch, resulting in a percentage error in g of 2.72.
  • To find the maximum error allowed in the value of g, the formula 4p s l / t s is used, with the percentage error in g calculated as delta g/g multiplied by 100, considering the errors in length, time, and s.
  • The error in the time period of a simple pendulum is determined by dividing the time for 100 oscillations by 100, not by 1, as the resolution of the wristwatch is 1 second, leading to a percentage error in g of 2.72.
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