Set 1

Transcript

0:00Introduction

Hello everyone! Here is a small puzzle before we start. Your screw gauge reads three point four seven millimetres for a plate. But with its studs closed, it showed a zero error of minus zero point zero four millimetres. So, is the plate three point four three millimetres thick, or three point five one? We will settle it in example two. This is our first mixed set on experimental skills, fifteen problems in the style of JEE Main. Reading these two instruments comes up often in JEE Main, so today we take two tools and two problems from this set. So, let's begin.

0:39Tool 1: the vernier callipers

Tool number one is the vernier callipers, so look at the figure. On top is the fixed main scale, marked in centimetres, and below it slides the vernier scale, numbered from zero to ten. The dark blue arrow marks the zero of the vernier, and the orange arrow marks the vernier division that lines up with a main-scale mark. Leave the reading beside them for now, okay? First, the least count. Let the letter n be the number of vernier divisions. When n vernier scale divisions, written VSD on screen, equal n minus one main scale divisions, written MSD, with n minus one in brackets, the least count, written L C, equals one MSD over n. Clear? Now let me ask you this. In the common laboratory callipers, ten vernier divisions equal nine main scale divisions of one millimetre each, and the m m on screen means millimetres. What is the least count? Yes, exactly, it is one millimetre over ten, which gives zero point one millimetres. That is zero point zero one centimetres, the c m on screen, the least count of our figure. Right? Now the reading. The main scale reading, written MSR, is the main-scale mark just before the vernier zero. The vernier coincidence, written V C, is the number of the vernier division that lines up with some main-scale mark. So the reading equals MSR, plus V C times L C, and the cross on screen means times. Got it? In the figure, the dark blue arrow shows the vernier zero just past two point three, so the main scale reading is two point three centimetres. The orange arrow shows the fourth division, so the vernier coincidence is four. Two point three, plus four times zero point zero one, gives two point three four centimetres, the same as the figure. With me?

2:34Tool 2: the screw gauge and its zero error

Tool number two is the screw gauge; look at this figure now. On the left is the main scale, also called the pitch scale, in millimetres. On the right is the circular scale, with fifty divisions, and it turns with the screw. The pitch is the distance the screw moves in one complete rotation, and here it is zero point five millimetres. Okay? So the least count is the pitch, over the number of divisions on the circular scale. Here that is zero point five over fifty, which gives zero point zero one millimetres, as written beside the figure. Right? The reading equals the pitch scale reading, written PSR, plus the circular scale reading, written CSR, times the least count. In the figure, the orange arrow points to the last visible mark, five point five millimetres, and division twenty eight lies on the long horizontal line, the reference line. So five point five, plus twenty eight times zero point zero one, gives five point seven eight millimetres. Clear? Now the zero error. Bring the two studs, the faces that grip the object, into contact, and the zero of the circular scale should sit exactly on the reference line. Notice that the numbers on the circular scale go up as you move up, twenty five, then twenty eight, then thirty. So if the zero sits below the line, is the zero error positive or negative? It is positive, yes, because the gauge already reads a little with nothing between the studs. Here n is a new count, the number of circular divisions between that zero and the line. So if the zero is n divisions below the line, the zero error is plus n times the least count. Got it? And if the zero is n divisions above the line, the error is negative, minus n times the least count. With me? Then, for every reading, the corrected reading equals the observed reading minus the zero error, and the zero error goes in with its sign, as the brackets say. Hold on to that, because example two tests it. Okay?

4:40Example 1: vernier reading when 20 VSD equal 19 MSD

Now, example one, which is problem one of the set. On a vernier callipers, twenty vernier divisions equal nineteen main scale divisions of one millimetre each. The main scale reads four point one centimetres, and the thirteenth vernier division coincides. We have to find the reading. Pause the video and try it first. Done? Okay, let's check. Here n is twenty, so the least count is one millimetre over twenty, which gives zero point zero five millimetres. With me? Now, the main scale reads four point one, and the vernier coincidence is thirteen. So the reading is four point one, plus thirteen times zero point zero five, isn't it? No, that is exactly the trap, because it mixes two units. Four point one is in centimetres, but zero point zero five is in millimetres. Ten millimetres make one centimetre, so the least count is zero point zero zero five centimetres. Clear? Now the units match. The reading is four point one, plus thirteen times zero point zero zero five. Right? Thirteen times zero point zero zero five gives zero point zero six five. And four point one plus zero point zero six five equals four point one six five centimetres. So the whole trick was to keep one unit throughout. Got it?

6:08Example 2: screw gauge reading with a -0.04 mm zero error

Now a harder one, example two, which is problem two of the set, and it is our opening puzzle. The screw gauge has a pitch of one millimetre, one hundred circular divisions, and a zero error of minus zero point zero four millimetres. For a plate, the main scale reads three millimetres, and the circular scale forty seven. We have to find the thickness. Pause the video and try it first. Done? Okay, let's check. The least count is one millimetre over one hundred, which gives zero point zero one millimetres. With me? So the observed reading is three, plus forty seven times zero point zero one, which equals three point four seven millimetres. Right? Now the zero error, minus zero point zero four. Many students simply take away zero point zero four, and write three point four three millimetres. Is that right? No, and this is the trap, because the rule says corrected equals observed minus the zero error, with its sign. So we write three point four seven, minus, and then the zero error in brackets, minus zero point zero four. Clear? Taking away minus zero point zero four is the same as adding zero point zero four. So three point four seven plus zero point zero four gives three point five one millimetres. There, our puzzle is solved: the plate is three point five one millimetres thick, not three point four three. So, as you see on screen, a negative zero error ends up being added. Got it?

7:45Quick revision: least counts, readings and zero correction

So, quick revision. For a vernier, the least count is one MSD over n, and the reading is MSR, plus V C times the least count. For a screw gauge, the least count is the pitch over the circular divisions, and the reading is PSR, plus CSR times the least count. And the corrected reading is the observed reading minus the zero error, with its sign, keeping one unit throughout. Now go and try the other thirteen problems of this set on this page. You can do this, all the best!