Overview

Transcript

0:00Introduction

Hello everyone! Okay, one small challenge before we start. Fifteen problems, twenty five minutes, and for every problem, you have to spot the idea yourself. Can you finish in time? Hmm, sounds tight, right? That is exactly what this chapter gives you: mixed problems in the style of recent JEE Main papers, from the whole of Unit One. Today I will show you how to use it like a real test, and then we will solve two problems together, with the clock running. So, let's begin.

0:31How this chapter works

So, first of all, what is inside this chapter? Three sets, and each set has fifteen original problems, written in the style of recent JEE Main papers, okay? Quick question. Three sets of fifteen: how many problems in all? Forty five, yes! Forty five fresh problems, all on Unit One. Set A is on units and dimensions. Find the unit of a strange combination, find the dimensions of a constant, decide which pairs of quantities match. Clear? Set B is on dimensional analysis and significant figures. Look, two different chapters in one set. One problem asks you to find a relation using dimensions, and another one wants an answer with the correct significant figures. So you cannot switch off. For every problem, first spot the idea. And Set C is on errors and instruments: percentage errors, vernier callipers, the screw gauge, and more. So between the three sets, the whole unit is covered.

1:35Treat each set as a timed test

Now the most important instruction of this chapter. Treat each set as a timed test: fifteen problems, in about twenty five minutes. So tell me, on average, how much time does one problem get? Let's work it out together. Twenty five minutes is twenty five times sixty, that is one thousand five hundred seconds. Divide by fifteen problems, and you get one hundred seconds per problem. And one hundred seconds is one minute and forty seconds. Less than two minutes, that's all! So the right formula must come to you quickly, and the calculation must be clean. That is the speed this chapter trains, okay? Now, here comes the trap. You are on problem six, you feel a little stuck, and you think, let me just take a quick look at the solution. You read it, you nod, and you feel, yes, I knew this! No, no, careful! That feeling is the trap. Reading a solution is not the same as solving the problem. So the rule is simple. Try the whole set first, as a test, and only then read the solutions. Your own answers, on paper, right or wrong. Then compare, and learn from every mistake. Got it?

2:47Topper's trick: read the badges

Now let me share a small trick that toppers use. Every problem on the page carries a badge: easy, medium or hard. Take Set A, for example: it has six easy problems, seven medium ones and two hard ones, okay? So, should every single problem get exactly one hundred seconds? Not really, right? One hundred seconds per problem is only the average. Some problems need much less, and some need more. So finish the easy ones fast and clean. The arrow on screen means, so: the time you save on the easy ones is extra time for the two hard ones. That is how you finish the whole set in about twenty five minutes. Simple and practical.

3:32Example 1: identify a quantity from its dimensions

Alright, now let's practise exactly the way this chapter says. This one is from Set A, and it is an easy one. Take energy into time, and divide it by mass into length squared. What does this quantity measure? Pause the video, write your answer, and then come back. Your hundred seconds start now. Done? Okay, let's check. First, write the dimensions of each piece. The square brackets on screen mean, dimensions of, okay? Energy is M L squared T to the minus two. Time is T, mass is M, and length squared is L squared, okay? Now the top: energy into time. T to the minus two, multiplied by T, okay? So T to the minus three, right? No, no, careful! This is the slip that costs marks. When you multiply, you add the powers. Minus two plus one is minus one. So the top is M L squared, T to the minus one. Clear? Now divide by mass into length squared, that is M L squared. The M cancels, the L squared cancels, and only T to the minus one is left. That's it! So now tell me, which quantity has the dimensions T to the minus one? Frequency, yes! Exactly. And look at the clock: a few short lines, well inside one hundred seconds. That is an easy problem done the easy way.

5:00Example 2: value of 1 newton in a new system of units

Now a medium one, from Set B, okay? Imagine a new system of units. Mass is measured in units of one hundred grams, length in units of ten centimetres, and time in units of zero point one second. In this system, what is the numerical value of a force of one newton? Pause the video, try it, and then come back. Done? Okay, let's check. First, which idea is this? Converting units with dimensions, correct! Force is MLT to the minus two. So n two equals n one, into M one by M two, into L one by L two, into T one by T two to the power minus two. Here n one is the number in S I, which is one, and n two is the number in the new system. M one, L one and T one are the old units, kilogram, metre and second, so old unit on top, new unit at the bottom, okay? Mass first. One kilogram is one thousand grams, so M one by M two is one thousand by one hundred: ten. Length: one metre is one hundred centimetres, and one hundred by ten is also ten. Now time. One second by zero point one second is ten. Ten squared is one hundred, so the answer is ten into ten into one hundred, ten thousand, right? No, no, careful! Look at the power again. The power of T in force is minus two, not plus two. So the time part is ten to the minus two, that is zero point zero one. See, this sign is the JEE trap. Always copy the powers straight from the dimensional formula. So n two is one, into ten, into ten, into zero point zero one. One! Look at that, one newton is exactly one unit of force in this new system. The mass and length ratios push the number up by a hundred, and the time part brings it down by a hundred. See how fast it is, once you spot the idea?

7:07Quick revision: three sets of 15, about 25 minutes each

So, quick revision. Three sets of fifteen problems, mixing all the ideas of Unit One. Each set is a timed test of about twenty five minutes, so about one hundred seconds a problem. And always try the whole set first, and read the solutions after. Now open Set A, start your timer, and begin. You can do this, I promise. All the best!