DC Pandey Basic Mathematics and Measurements Solutions

DC Pandey Mechanics Part 1 Solutions for ‘Basic Mathematics and Measurements’ will take you through the basics of measurements and the errors that occur while measuring certain entities and values. In this chapter of DC Pandey Physics, you will learn about permissible errors, maximum error, least count, and proportionality. Once you engage with the chapter you will be able to detect errors in percentage values, work with the proportionality of different measurements, decrease measurements by certain mentioned values, find the least count of the main scale, observe the number of divisions of a circular scale etc. 

DC Pandey Solutions for Mechanics Part 1 ‘Basic Mathematics and Measurements’ comprises of an exercise with and has a total of 51 questions. The questions are related to percentage increase, rounding off digits, percentage decrease and error detection in case of various quantities like kinetic energy, pressure, volume, length, breadth etc. The exercise questions include problems where you are required to apply the formula and accordingly derive the required values. The book aims at strengthening your concepts for high-level competitive exams like JEE and NEET. These competitive exams have a considerable amount of questions from this chapter.

Instasolv has formulated DC Pandey Mechanics Part 1 ‘Basic Mathematics and Measurements’ Solutions for all questions. The solutions have been derived by subject experts who understand the requirements of the students and have come up with the best possible ways to solve these questions. With the help of these solutions, you will be able to brush up your concepts and gear up to face the competitive exams. 

Important Topics for DC Pandey Mechanics Part 1 Chapter 1: Basic Mathematics and Measurements

Least Count 

In this chapter, you will be introduced to the concept of least count. Least count is the term given to the smallest measurement which can be taken from any instrument. You will learn to derive the least count from the main scales of different instruments like vernier callipers and screw gauge. This concept is not only important theoretically but will also help you in rectifying measurement errors during your practical exams. Least count tends to render the calculation due to the minute difference in the measured values, therefore it is essential that you learn to find it and use it to omit any such glitch from your calculations. 

Least count = smallest reading of the main scale / total number of divisions on the instrument scale

You can also understand least count as the difference between one smallest reading from the instrument scale. 

Zero Error  

This error occurs when the reading of the instrument, say for example vernier calliper is a positive or a negative reading away from the original reading of 0.00 mm when the instrument is closed (basically when it is at its original closed position). In case if the zero error is in the positive direction it means that the instrument is giving a positive reading away from the 0.00 mm position and in case of a negative zero error, it means the reverse. This concept will also help you while performing your practical exam and omitting any kind of calculation errors which can occur.

Logs, Integration and Trigonometry

You would have studied all of these concepts in your previous classes. In this chapter, you will get to revise these concepts and learn how they are used very frequently in the upcoming chapters while working with numerical problems. The basic formulas and values related to integration, differentiation, logs and trigonometry have also been provided for you to learn and save time by applying them while solving questions. 

Percentage Increase and Decrease

This is a very basic concept that you would have learnt in your junior classes. In this chapter, you will apply the same fundamentals and calculation process to find the percentage difference in the case of force, acceleration, energy, power etc. You will have to combine the formula of these quantities along with the percentage calculation to determine their increasing or decreasing value. 

Exercise Discussions of DC Pandey Mechanics Part 1 Chapter 1: Basic Mathematics and Measurements 

The chapter contains four kinds of exercises, details of which are given below:

Section I 

  • This section contains four types of exercises that include single correct option questions, more than one correct option questions, assertion and reason questions and matches the column question. There is a total of 21 questions in this section. 
  • These questions revolve around concepts like maximum error measurement, least count of the main scale, sign conventions through the scale and percentage alterations.
  • All these questions are based on the basics from the chapter and utilize the introductory fundamentals from it. 
  • There is one question that requires you to detect the maximum percentage error for the given variable x. 
  • Assertion and reason exercise contains a question where you are then required to analyse the given statements and assert whether both of them are true or false or if any one of them is true and the other is false. You are also required to provide a proper explanation for your assertion.
  • In the match the column question you are required to perform differentiation and other mathematical operations on either of the given set of information. 

Section II

  • This section contains subjective questions on topics like trigonometry, calculus, graphs, significant figures, error analysis and Vernier Callipers and screw gauge. 
  • You will be solving questions to find the mean values, absolute errors in measurement, fractional error, and percentage errors. 
  • There are questions regarding rounding off to four significant digits, plotting graphs when values of y or x are decreasing exponentially, differentiation and integration. 

Why use DC Pandey Solutions Mechanics Part 1 Chapter 1: Basic Mathematics and Measurements 

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