Zero Error and Backlash of a Screw Gauge

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. I take a screw gauge, and I close the studs gently, with nothing at all between them. So the reading should be zero, right? But the circular scale shows division five on the index line. Hmm, is the gauge broken? Should we throw it away? And here is something even stranger. Sometimes, to correct such a gauge, you subtract the error, and your answer goes up! How can subtracting make a number bigger? Today we will settle both puzzles. And remember, zero error questions come in JEE again and again, and the sign is exactly where students lose marks. So, let's begin.

0:43Positive zero error: zero below the line

So, first, how do we even check for a zero error? Close the studs gently, and use the ratchet for it, okay? Not by force. Then look where the zero of the circular scale sits, compared with the index line on the main scale. Look at the left picture. The zero of the circular scale has gone below the index line, and division five sits on the line. In general, we call that division small n, okay? Now think. With nothing between the studs, this gauge already shows five divisions. So, is every reading of this gauge too big, or too small? Yes, too big! It has counted five divisions before the object even comes in. So we call this a positive zero error. Zero error equals plus n, times L C, the least count, okay? Here, plus five divisions, just as the picture says. So our gauge from the start is not broken at all. It simply has a positive zero error. Clear?

1:43Negative zero error: zero above the line

Now the right picture. Here the zero of the circular scale stays above the index line. It has not come down far enough. So the division on the line is a big number, near the end of the scale. If the circular scale has capital N divisions, we write that division as N minus m, okay? Here, in the picture, the circular scale has one hundred divisions, and ninety five is on the line. So the zero error is plus ninety five divisions, right? No, no, careful! This is the JEE trap. The zero is short of the line, so this gauge reads less than it should. The zero error is negative: minus m, times the least count. Count how far the zero is from the line, not the number written on the line. Got it? So here, m equals one hundred minus ninety five, that is five. Zero error, minus five divisions, exactly as the picture shows. Look, ask one question every time: is the zero below the line, or above it? Below means plus, above means minus. With me?

2:48Correcting the reading

Now, how do we use the zero error? Quick recap first. Least count equals the pitch, divided by capital N, the number of circular divisions, okay? And the observed reading is the main scale reading, plus the circular scale reading times the least count. On screen, MSR is the main scale reading, and CSR is the circular scale division on the index line. Then, just one rule. Corrected reading equals observed reading, minus zero error. Always minus, and put the zero error in with its own sign. Now our second puzzle. Suppose the zero error is negative, and you subtract it. Does the answer go up, or down? Yes, up! Sounds strange, right? Let's see why. See, minus of minus m times least count is plus m times least count. Subtracting a negative error adds it on. Perfectly logical. The gauge was reading too little, so the correction pushes the answer up. You will see it with real numbers in Example two.

3:53Backlash error

One more error, and this one hides inside the screw itself. It is called backlash error. When a screw gets worn, it may turn a little without advancing at all. When does this happen? When you reverse the direction of rotation. The screw turns, the circular scale changes, but the screw has not moved forward. So that reading is simply wrong. Alright, tell me. While taking a reading, you went a little too far, and turned the screw back. Can you trust that reading? No! You reversed the direction, so backlash can creep in. So here is the topper's habit. Always turn the screw in the same direction while taking readings, closing on the object every single time, okay? And always use the ratchet, so that the studs are not over-tightened, and the same gentle pressure is applied each time. That's it, two simple habits, and backlash cannot spoil your readings.

4:49Example 1: wire diameter with a positive zero error

Got it? Right, on to Example one. So, a screw gauge has a pitch of zero point five millimetre, and fifty circular divisions. With the studs closed, the fifth division is on the index line, and the circular scale zero is below the line. Measuring a wire, the main scale reads two point five millimetres, and the circular scale reads twenty. Find the diameter. Pause the video, and try it first. Done? Okay, let's check. Least count first: zero point five divided by fifty, that is zero point zero one millimetre. The zero is below the line, with five on it. Below means plus, right? So the zero error is plus five times zero point zero one: plus zero point zero five millimetre. Observed reading: two point five, plus twenty times zero point zero one. Two point five plus zero point two: two point seven zero millimetres. Now correct it. Observed minus zero error: two point seven zero minus zero point zero five. Two point six five millimetres. The gauge was reading too much, so the true diameter is a little smaller. Makes complete sense.

6:04Example 2: ball bearing with a negative zero error

Now a harder one, JEE level. Read it with me. The main scale of a gauge shows one millimetre of advance for two rotations, and the circular scale has fifty divisions. With the studs closed, its zero is three divisions above the index line. Then a ball bearing reads three point five millimetres on the main scale, and forty one on the circular scale. Find its diameter. Pause and try. Hint: find the pitch first. Done? Okay, let's check. Careful, the pitch is not one millimetre. One millimetre for two rotations, so one rotation gives zero point five millimetre. That is the pitch. Then the least count is zero point five by fifty: zero point zero one millimetre. The zero is above the line, so the error is negative, okay? Three divisions: minus three times zero point zero one, that is minus zero point zero three millimetre. Observed reading: three point five, plus forty one times zero point zero one. Three point five plus zero point four one: three point nine one millimetres. Now correct it. Three point nine one minus zero point zero three, so three point eight eight, right? No, no, wait! That is exactly the trap. The zero error is minus zero point zero three. Observed minus zero error means three point nine one, minus of minus zero point zero three. So we add: three point nine four millimetres. Look, we subtracted the error, and the answer went up, from three point nine one to three point nine four. Our second puzzle, with real numbers!

7:48Quick revision: zero error correction and backlash

So, quick revision. Zero below the line: plus n times least count. Zero above the line: minus m times least count. Corrected reading equals observed reading minus zero error, with its sign. And for backlash, turn the screw one way only, and use the ratchet. So that gauge showing five with the studs closed was never broken. You just correct it. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!