Unit Test

Transcript

0:00Introduction

Hello everyone! Okay, one small challenge before we start. Fourteen questions, from Chapters One to Six of Unit One: dimensions, significant figures, errors, the vernier and the screw gauge. And at the end, only the answers. No worked solutions. So if your answer does not match, nobody explains it to you. Can you still score fourteen out of fourteen? Hmm, a little scary, right? But look, this is exactly how the JEE paper feels. It mixes all the ideas of the unit, and no question tells you which chapter it comes from. Today I will show you how to take this unit test like a real exam, and we will solve two of its questions together. So, let's begin.

0:47What the unit test covers

So, first, what exactly is inside? Fourteen questions, and below them, one Show answers button. Only answers, okay? No worked solutions. So who checks your working? Yes, you do! The checking is your job. Questions one to six are on units and dimensions: dimensional formulae, converting units, changing the base quantities. That is Chapters One, Two and Three. Questions seven to eleven are on significant figures and errors, Chapters Four and Five. Counting significant figures, the error in a formula, and a pendulum experiment. Questions twelve and thirteen are on the vernier callipers and the screw gauge, from Chapter Six. And question fourteen is an order of magnitude estimate, from Chapter One. So all six chapters, One to Six, are in there.

1:42Take it like the real exam

Clear? Now, how should you take this test? Like the real exam, with a timer. Chapter Eight's overview gives a timing guide, and the wavy equals sign on screen means about. So: about two minutes for an easy problem, three to four minutes for a medium one, and six to eight minutes for a hard one. And write all fourteen answers on paper first. Your own answers, right or wrong. Got it? Alright, now the trap. You are on question three, you feel a little stuck, and you think, let me just check this one answer, right? So you press Show answers. No, no, careful! That button opens all fourteen answers together. One small peek, and you have seen the answers to the whole test. So keep it closed till the very end. And when an answer does not match? Don't just read the right answer and move on. Go back to the chapter that question came from, solve it again, and then compare. That is how a test teaches you. Clear?

2:47Topper's trick: name the idea first

Now let me share a trick that toppers use. In the real paper, no question tells you its chapter. So before you write a single number, name the idea, and the chapter it comes from. Then you know exactly which formula to use. Let's try. Question five: the period of a mass on a spring depends on m and k, the mass and the spring constant. Which idea is this? Deriving a relation by dimensional analysis, from Chapter Three, that's right! The arrow on screen means, so. Write the period as a product of powers of m and k, and match the dimensions, okay? Next, question ten. Two lengths are subtracted. So the errors also subtract, right? No! Sum or difference, the absolute errors always add. That is Chapter Five. See, this one idea decides the whole question. And question fourteen, the number of seconds in a year? Order of magnitude, from Chapter One. That's it, three questions, three ideas, and not one number written yet.

3:54Example 1: least count of a screw gauge

Alright, now two questions from the test itself. First, an easy one, question thirteen. Here is a screw gauge that advances two millimetres in four full turns, and its circular scale has one hundred divisions. Find its least count. Name the idea, then pause the video and try it. Done? Okay, let's check. The idea: the least count of a screw gauge, Chapter Six. Two millimetres, one hundred divisions, so the least count is two by one hundred, zero point zero two millimetre, right? No, no, careful! That is the trap. Look at the figure: the main scale, and the thimble carrying the circular scale. Those two millimetres took four full turns, not one. So first find the pitch, the distance moved in one full turn: two millimetres by four, zero point five millimetre. Now, one full turn of the thimble is one hundred divisions. So the least count, L C, equals the pitch by N, the number of circular divisions: zero point five millimetre by one hundred. Zero point zero zero five millimetre. Absolutely correct, and it matches the answer key. Pitch half a millimetre with one hundred divisions is one of the typical screw gauges of Chapter Six, so this number should feel familiar.

5:13Example 2: percentage error in g from a pendulum

Now a harder one, question eleven. Read it with me. Here a pendulum completes twenty oscillations in forty point zero seconds, plus or minus zero point two second. Its length is ninety nine point zero centimetres, plus or minus zero point one centimetre. Find the percentage error in g, okay? Pause the video and try it. Done? Okay, let's check. Which idea? Errors in a standard experiment, Chapter Five, exactly! g equals four pi squared l, over T squared. Four pi squared is a constant; it carries no error. And T is squared, so its relative error counts two times. The little triangle, delta, means the error. So delta g by g equals delta l by l, plus two times delta T by T, okay? Length first. Zero point one by ninety nine point zero: about zero point one percent. Simple. Now the period. Forty seconds for twenty oscillations, so T is two seconds. And the error is zero point two second. So the error in T is zero point two by two, ten percent, right? No, no, careful! This is the JEE trap. That zero point two second is the error in the total time of forty seconds, not in one period. T equals small t by twenty, so the value and the error both get divided by twenty. The relative error stays the same: zero point two by forty point zero, zero point five percent. With me? Now put it together. Zero point one percent, plus two times zero point five percent. One point one percent! Exactly what the answer key says. And notice: the period, entering squared, gives one percent, while the length gives only zero point one. So to improve this experiment, improve the timing: time more oscillations.

7:13Quick revision: how to take the unit test

So, quick revision. Fourteen questions, all of Unit One, with answers only. For every question, name the idea and its chapter first, then calculate. And write every answer before you open the answers. Two questions we did together; twelve are waiting for you. Now try the unit test on this page, with your timer on. You can do this, I promise. All the best!