EXAM TDB CLASS, DAY 1...

Added: 2026-06-03

[00:00:27]Hello. Can we see? Are we active now?

[00:00:29]Can we see the board queen? Can you see the body?

[00:00:45]Okay.

[00:00:46]All right. Let's start.

[00:01:10]dimension analysis.

[00:01:16]Now um one thing you need to know is that um when we talk about dimension we have to talk about quantity and unit themselves. So you don't need to spend much time with that but something we are familiar with. Now quantity like force velocity acceleration etc. Now and we know they are units.

[00:01:39]Now for dimension dimension we use dimension to show the relationship between a physical quantity and some fundamental quantities. And what are those fundamental quantities?

[00:01:53]Mass, length and what?

[00:01:56]These are the only three fund. No, we have about seven or eight fundamental quantities. These are the only three fundamental quantities that we use that um we relate to other physical funds in terms of dimension. What dimension does is that it shows the relationship of physical fun like force relationship between force and all these three fundamental quantities. So dimension show the relationship. So that's just the definition not sure. So now let's start with some um basic concepts and for you when we talking of dimension if you don't know the unit of a quantity you cannot derive the dimension for instance force or if you don't know the formula if I were asked to find if I was asked to find the dimension of force I don't know that force mass time acceleration which is same thing as kg m/s squ I can't know that the dimension is what N lus no m for mass L for length which is this meter this is for the mass and this second is for the big so that's just that's that that's you ask me something now let's start from the verification of the equation of motion So you can use dimension to verify some physics equations if they are valid or not. Whenever I use dimension to verify some equation they are not valid and both sides are not equal that means the equation is not valid. For instance if I'm adding quantity a to b and I'm deducing that equal to quantity c it means that both a and b have the same dimension and they also have the same dimension as c because they don't have the same dimension. I can't add I cannot add force is acceleration. I can only add the same quantity together. So for me to add the same quantity together that mean the same direction. Same thing applies to negative to subtraction. Are we together? I can't subtract velocity from time. I can only subtract velocity from velocity. Which means for subtraction to be valid in physics. That means what are subtracting from each other they have the same dimension. And what they equal to also have the same.

[00:04:19]If I subtract velocity from velocity will I get acceleration?

[00:04:23]velocity. So whatever they must also have the same dimension as I clear I wanted to say something.

[00:04:34]Now if I say subtract, if I say 2 a - 2 b equals to what? Where a and b are in meters?

[00:04:50]Find the direction of 2 a and 2 b.

[00:04:52]What's the answer?

[00:04:54]If a and b are in, what's the answer to this guy?

[00:05:00]Okay. 2 a and 2 a where a is in meters.

[00:05:08]>> What's the dimension?

[00:05:20]It's not zero. Actually, this is 2 a - 2 a. Since a is a meter, that is 2 m - 2 m, which give us 0 m. Are we together?

[00:05:34]What's dimension for zero?

[00:05:37]One. What's dimension for me? So what are we together? So that all numbering zero they have dimension of one. So whee you are doing basic arithmetic the dimension is equal to the individual dimension it's less concerned with coefficient once you doing basic arithmetic not just basic arithmetic basic arithmetic that involve addition and subtraction alone alone not division and multiplication are we together now if If a square + b = where z is in meter where z is in meter.

[00:06:40]Find the dimension of B. Dimension of A, B, and what? And C. Let's Let's try it.

[00:06:47]Let's try it.

[00:06:52]That's class. Let's try it. If a square b= Use that. Nice.

[00:08:39]This is Hallelujah.

[00:09:26]It is time.

[00:09:46]Okay.

[00:09:56]Galaxy.

[00:10:36]Okay, let's do like this.

[00:11:03]I didn't hear Answer question.

[00:12:07]Hello Zoom Are we What is the answer?

[00:13:06]>> A is what?

[00:13:11]>> LT minus 2. What about B?

[00:13:15]>> B is what?

[00:13:19]>> C.

[00:13:24]>> Okay. B is L and C is L.

[00:13:35]So BC = L that is V = LCU and C = LBUS don't know what B and C is like this for >> Yeah. Yeah.

[00:14:13]>> Dimension.

[00:14:15]>> Can I help all these guys not slept?

[00:14:23]>> Don't go.

[00:14:32]Let me >> call the question.

[00:14:39]>> Okay.

[00:14:41]>> Given that the quantity s >> S= >> which S?

[00:14:47]>> S capital S >> Uhhuh.

[00:14:49]>> is equal to A into >> given that the quantity S which represents speed.

[00:14:58]>> Speed speed >> is equal to a bracket 1 - e^ - x >> 1 - e^ - e no >> d x and x is displacement.

[00:15:23]Uhhuh.

[00:15:24]>> Find the dimension of the reciprocal of >> Find the dimension of the reciprocal >> of B that is 1 / B again. A >> 1us B.

[00:15:48]Now and x is displacement.

[00:15:54]Now for dimension you cannot have a quantity raised to power quantity the power must be the power must have a dimension of one. Do we get any power you have on top of quantity must have a dimension of one. Am I communicating? So which means all this power must be what?

[00:16:17]>> One. So - b xt = what? Are we together?

[00:16:23]>> So that means - = what? 1 xt. That means b = - 1.

[00:16:32]Dimension has nothing to do with minus.

[00:16:36]Are we together?

[00:16:38]>> So 1 / b = what?

[00:16:40]>> x. Which is what?

[00:16:44]Is that the option?

[00:16:46]>> Yes. That's the correct answer. Do we understand?

[00:16:57]The power of a quantity always have dimension of one. The power of a quantity. The dimension must be one. It is d power is always dimensionless. And dimensionless means dimensionals to one.

[00:17:11]So minus b xt = what? One. Are we together?

[00:17:17]>> So minus b = what? 1 xt.

[00:17:22]Right.

[00:17:23]>> That means b will give us what? Minus what? 1 / xt.

[00:17:29]That means and we have to find the reciprocal of b which is 1. So 1 / b will give us xt isn't it? Are we together?

[00:17:41]Dimension has nothing to do with negative sign. What's for whe >> Yeah. Yeah. Yeah.

[00:18:01]Okay, let's move on. They are following.

[00:18:05]Second question.

[00:18:08]>> Okay. Do you guys do you understand this one just did?

[00:18:15]Second question.

[00:18:16]>> Okay.

[00:18:18]The position of a particle at time is given by x of t.

[00:18:23]The position >> of a g particle >> is given the position of a particle at time t >> is given by s of t >> uh >> is equal to a b.

[00:18:39]all into 1 - >> yes >> find what >> where a is the constant >> find the dimensions of a and b respective is a constant so we have to find the dimension of that constant And >> sharp.

[00:19:13]>> It's not sharp but sharp actually.

[00:19:15]>> And they said a is like the greater than. They wrote it twice.

[00:19:24]>> Far far greater than >> zero.

[00:19:28]>> Okay. Like a is far far greater than zero. Are we together?

[00:19:33]We ask that a is constant and we should find the direction for a >> and b this mean whenever I see double sign like this far far greater than or this is far far less than so here we have x of t this position mean the left hand side is l right so here we have l= let's open the bracket a b minus what a b cus what bt Are we?

[00:20:03]>> Yes.

[00:20:05]>> A B= what?

[00:20:07]>> L. Am I right?

[00:20:09]>> So the dimension for find direction for A and B. Okay. Okay.

[00:20:15]So A. Now A will give us what? LB.

[00:20:20]Are we together? If we cross multiply.

[00:20:23]A will give us LB and B will give us what?

[00:20:27]Make the formula. What do we get?

[00:20:32]A L but we need to find B since we have power hereus BT = 1. Do we remember?

[00:20:42]>> Yes.

[00:20:42]>> So here we have - B = what? 1 / T. B = - 1 / T = 1 / big T. Dimension has nothing to do with minus.

[00:20:55]So our B is 1 / BT.

[00:20:58]Are we together?

[00:21:01]Yes.

[00:21:01]>> So that our equals what? L * 1 / C. And that's what party.

[00:21:10]>> Yes.

[00:21:11]>> Is there should be there?

[00:21:18]>> The first option is let's finish it first.

[00:21:28]So that's our A for our B = L T and our A is part >> the answer is not on the >> CUS the answer is not on the but this is correct answer do we understand how >> constant does not mean dimensionless is it constant or Does it have dimension?

[00:22:00]>> Do we get constant is different from number? No number is also a constant.

[00:22:05]When they say constant, they don't mean is dimensionless. Do we get? So you can have constant and yet not dimensionless for which we also have them constant plenty. Now >> this guy is not actually constant. It varies with altitude though it doesn't exceed 9.8 and 10 >> constant constant yet can get the dimension do you understand when they say constant even me then when I constant dimension but that's it's only dimension if the constant is a number a constant a quantity can be a constant take note of they are saying the displacement depend on time it's not that you are multiplying it's a function of time that if you have your t can just subt that is not time writing it like this depends on time. Do we get it's not maybe you like that I can just write it as x but put something like this depends on time if you are given the value of time you can get your x by substituting time if it doesn't depend on time you have time you can substitute it you get so it depends on time such that you have your time just >> is there more question there >> I give you guys one more question.

[00:23:56]>> The the period.

[00:24:14]The period of vibration of a liquid.

[00:24:17]The period of vibration of a liquid.

[00:24:21]The period of vibration of a liquid depends the period of vibration of a liquid depends on its density P. It's not like P like row is it row or whatever it just looks like.

[00:24:39]The kind of vibration of a liquid depends on it density P radius R and surface tension T. It's not like that's sign for use.

[00:24:53]It's not I'm using the symbol of the period of vibration of a liquid depends on it density P radius R and surface tension T.

[00:25:04]Deduce an expression.

[00:25:08]Yeah.

[00:25:11]Stop. Deduce an expression for the period of vibration using dimension analysis.

[00:25:22]Deduce an expression for the period of vibration.

[00:25:27]Using dimensional analysis.

[00:25:30]Deduce an expression for the period of vibration using dimensional analysis.

[00:25:36]Do you get the question?

[00:25:40]The vibration of a liquid depends on it depends on it surface tension t density P and radius R. Whether you mention density first no problem. Did this an expression for the period of vibration using dimensional analysis?

[00:25:59]Are we together? Whenever I see the word depends under direct means directly proportional but I didn't know >> and just I know if something if something is inversely proportional they also depend on each other they depend. So whether in but in dimension whenever I see the word depend is only meant for directly proportional.

[00:26:33]So the period of vibration no period is also time depends on what density also depends on radius also depends on what surface tension. So t depends on what density r and what >> are we together? Do we get that? So yeah, we can say T equals what? K P R T.

[00:27:04]Is that clear?

[00:27:06]>> Anything you want to do, we are not touching K. K, we just stay there till we end because it's constant.

[00:27:13]So here now label all this P RJ. So T aside, I don't want you to disturb me. T= P.

[00:27:30]If there is more continue D if there are more are we together. So here now we have T = Pity Lass.

[00:27:46]So here we have m lus power a l b sorry tension rather >> that's force per unit length force is mass time acceleration force per unit length and force is mass time >> acceleration are acceleration that's mus so is M mtus 2^ what c. So here we have t = what? M power a minus 3 a. Are we together?

[00:28:27]Open the bracket. N power cus 2 c. Right?

[00:28:39]I have m l and t but I only have t. So I want to write this to have m and l m^ 1 = what m^ - a m^ c - 2 c are we together these two are just one I'm not change anything so I want to compare both sides so on this side m on this side equals to what m^ A m* what? M power c.

[00:29:16]So we have m^= what? m^ a + c. Are we using indices? So here we have 0 = what?

[00:29:29]So a= what? C. Are we together? Now for l= what?

[00:29:39]Lus 3 a= 3 a something is missing okay we still have b sorry - 3 a there's l here so we have - b so here we have a^ - 3 a + b. So we have 0 - 3 a + b. So we have 3 a b. So a b / 3. Are we together?

[00:30:31]Now the last one. C^ 1 = what?

[00:30:36]- 2 C. So 1 = - 2 C. So C = what? - 1 / 2.

[00:30:48]So here now we have a C c is - 1 / 2 that means a is 1 / 2 sorry if a = minus c that means c = minus a. Are we?

[00:31:02]>> Yes.

[00:31:04]>> Okay. There is no A=US.

[00:31:09]So A= 1 / 2.

[00:31:12]It is B that we need to make for we've got A and C. Now we c minus A. Now B= 3 A. Are we together? So you don't need to make.

[00:31:26]So B= 3 A 1 2 which is what?

[00:31:31]>> 32. Right? So now the period of vibration t don't forget was what k r is what k what's a 1 / 2 r 2 c >> what is common to all the power >> yeah okay Sorry, sorry. V is 3 / 2. C is - 1 / 2. What's to the power?

[00:32:11]1 / 2. So here you have R3 - 1.

[00:32:18]Isn't it you get this back? You get this back.

[00:32:23]You get this back. Are we together? So here you have t= what? K. This becomes root.

[00:32:33]density rqus.

[00:32:36]So here you have t = what k root density rub what >> that's it and should I tell you the formula for period of vibration this is even the formula so can you even use dimension to derive a formula in physics so that's the expression for the period of vibration do we get that >> who doesn't Understand?

[00:33:10]Just apply just put ABC there.

[00:33:14]Compare the two sides. Do your indices.

[00:33:23]1 2 3 4 5 six minority are sleeping. So let's continue then.

[00:33:40]Do we get that those who are watching online?

[00:33:47]I hope it's clear.

[00:33:55]Do we have any past question from dimension here?

[00:34:00]>> You have one Yeah. Yeah. Yeah. We need them too like very much those words. We need them. Now let's write this so I can clean the board.

[00:34:48]How are you doing?

[00:35:09]dictates that question.

[00:35:17]Which of the following statements is or are false?

[00:35:23]>> Which is or are false? H statement one.

[00:35:26]>> All these quantities in mechanics are about two in number.

[00:35:32]>> All this >> all base.

[00:35:34]>> Okay. All base >> these quantities in me are about two in number.

[00:35:41]the person.

[00:35:43]>> Statement two, a measured quantity without >> methics are >> about two >> about two in numbers.

[00:35:55]Statement two.

[00:35:56]>> A measured quantity without unit has incomplete unit. A measure quantity >> without unit has incomplete.

[00:36:08]>> Without unit >> as incomplete meaning >> incomplete >> meaning >> all physical happenings are physical quantities. All physical. This is your test question.

[00:36:29]>> Physical quantities.

[00:36:31]>> Physical quantity.

[00:36:33]>> A quantity that has no dimension but has its units as a supplementary quantity.

[00:36:42]>> That has no dimension.

[00:36:47]But as unit is known as supplementary quantity but as unit is known as supplementary >> is known as supplementary.

[00:37:06]So which one is false? A is false right?

[00:37:09]Let's delete that first. So these are part of a me quantity without unit.

[00:37:15]Sorry. Sorry. All base quality in matrix are about three numbers. No no base fundamental about eight or eight fundamental. So this is wrong. A measure quantity without even has incomplete meaning trueity.

[00:37:43]The me quantity without unit has incomplete minutes.

[00:37:48]>> It's true.

[00:37:49]>> It's not much true. If there's no unit, no. Then we used to say, what do we used to say there?

[00:38:02]Then we used to say the unit is meaningless.

[00:38:07]It's not meaningless. Just that it's incomplete. Are we together? It's not meaningless. A quantity without unit are also called pure numbers. You should take note of that. Pure numbers. A quantity without also called pure numbers.

[00:38:22]So pure numbers are not unit they are not meaningless rather just that they are incomplete. Take note of that. So a measure quantity without unit has incomplete meaning is true.

[00:38:35]>> The meaning is not meaningless but the meaning is incomplete. So this is true.

[00:38:39]This is false. This is true. All physical happening are physical quantity. Yes or no?

[00:38:54]physical physical quantity of check butch and things that are all happening physical quantity.

[00:39:29]two of us.

[00:39:32]We are coming back to that. I not me it's my family.

[00:39:36]A quantity that has no dimension but has unit is known as supplementary quantity. First of all, what the meaning of supplementary?

[00:39:56]A quantity that has no dimension but has unit is known as supplementary quantity.

[00:40:04]Even before this is possible >> but what's the meaning of supplementary >> like adding things together >> like additional >> so that has no dimension but has unit is like an additional quantity >> like it's not possible.

[00:40:27]>> Yeah, that's false actually obviously.

[00:40:30]Now let's check theory. All physical happening are physical quantities.

[00:40:39]This is true.

[00:40:43]Go and check.

[00:40:45]>> What number is that?

[00:40:50]What number? What number of question is that? Neither should be one or what number of question is that?

[00:41:00]It's false now said statements two only one and two only one two and four and only two and four >> come back is there one only sir >> according to this supplement supplemental quantities It's known as supplementary I was saying is known as as it's supplementary.

[00:41:39]Okay. Okay. So this is true.

[00:41:43]Is there one only the option? That's what I'm asking.

[00:41:46]>> There's no one only.

[00:41:49]Read the options again.

[00:41:56]Two, >> one and two only.

[00:42:00]>> One, two, and four.

[00:42:02]>> Two and four.

[00:42:04]Two, three, and four.

[00:42:06]>> This one is true.

[00:42:15]>> This is true.

[00:42:19]>> I've seen this in past question before.

[00:42:22]Even the man said it a quantity is true. It cannot be false. Two cannot be false.

[00:42:34]Is there one and three there?

[00:42:42]>> One and two only.

[00:42:44]>> What number? What number? That's your test.

[00:42:47]>> No.

[00:42:47]>> Okay. It's not your test.

[00:42:49]And I'm just disturbing myself. I thought this your test now that I want to confound like where did you see it?

[00:42:56]>> It's like a tutorial question.

[00:43:00]I hope it's not my own tutorial question. Two is correct. I've seen it in past question before. Two cannot be false. A quantity without unit has incomplete meaning. It's true. It has incomplete meaning. That was true.

[00:43:15]It's even the man said it. The mind professor aware >> not that it's meaningless.

[00:43:21]>> The question is not correct.

[00:43:23]>> Yeah. Yeah. So two is correct. Should be one only.

[00:43:28]>> Should be one only. So one only is false. So please this guy is true. Two is true. I hope that's clear. Now true is not false. The quantity without unit is not meaningless. Just that the meaning is not complete.

[00:43:46]Also take note of this supplementary quantity quantity with dimension.

[00:43:54]>> Do we have another question there like words like this?

[00:44:01]>> So it's been confirmed but okay. All right. The next question.

[00:44:12]>> The next question. The following statement is or are correct.

[00:44:16]>> Uhhuh. Statement.

[00:44:18]>> The ratio of distance to displacement is always one for a body moving.

[00:44:30]>> The ratio of distance.

[00:44:32]>> Let's examine it one by one as he's saying it.

[00:44:35]>> The ratio of distance to disment is always one for a body moving with uniform speed. The ratio of distance to displacement is always one for a body moving with uniform speed. Is that true?

[00:44:49]Now first of all, what is uniform speed?

[00:45:04]I'm coming.

[00:45:12]>> Yeah, we can have uniform uniform. I think uniform is same thing as constant.

[00:45:17]Now we can have uniform speed in a circular motion >> where speed is constant but velocity changes. So since uniform speed is not only attached to straight line motion the ratio of distance and displacement is not always one. Assuming it's only a straight line then distance equals to disment for a straight line motion distance will be one. Since you can also read the question again >> the ratio of distance to displacement is always one.

[00:45:47]>> It's always it's not always but in circular motion is not one because we can have uniform speed in circular motion. So that one is first. Question two. current is >> even there is a topic in that in your slide uniform circular motion when we talk about uniform speed. So since we have uniform speed in circular motion displacement is not equal to distance.

[00:46:10]So it's not always but at times it can be due to straight line motion. So question B >> current is a fundamental quantity why charge quantity not because charge as a quantity depends on current >> actually charge does charge I think charge depend >> well the first part is correct >> current is fundamental charge is derived continue that >> not because charge as a quantity depends on current >> charge actually depends on current yeah because a Current need to pass through a cycle before it can store a charge. Are we together? So charge depends on current actually and we also have we together. This is the fundamental >> still not because >> okay wait >> he said is a fundamental quantity why charge is a direct quantity not because charge as a quantity depends on current >> okay okay I get I get I get >> it's true the thing is that not that this guy doesn't depend on current it depends But that's not just that's not the only reason why it's a derived we can derive charge without current let me just let me let me get a formula that can combine charge together no we have Q= C >> do we remember there's no current capacitor do we get what we saying so not because it's actually a direct not because it depends on point actually that's so that's also true what's the next one >> human body can never act as an asel as >> human body cannot >> can never act as an as a Accelerometer that is what we used to acceleration but as a speedometer human body >> let's check >> call the next the next statement first before we down >> then the next one a body may beated even when it is moving uniformly body.

[00:48:57]>> No, that's false. That one is false.

[00:49:00]>> Uniform uniform motion there's no false.

[00:49:04]>> So one and two. Let's check that three very well. Woman body number three. One and two are true. Now let's check if three is also true.

[00:49:14]read number three very >> human body can never act as an accelerometer >> which mean they saying we cannot use human body to measure acceleration but >> but as a speedometer >> is that is that not force I'm coming if body can measure speed be able to measure acceleration It's false.

[00:49:53]>> Two and three. Yes, it's correct.

[00:49:57]>> What did they question before? Which of statements are correct?

[00:50:22]is one. I thought one is correct.

[00:50:26]>> No, one is one I talked about for a body moving with uniform.

[00:50:30]>> Okay. Okay. One is not correct.

[00:50:32]>> But two is >> okay. Two is correct.

[00:50:38]>> Okay. You are saying something.

[00:50:51]Yeah. Yeah. Yeah.

[00:51:02]>> He said acceleration.

[00:51:16]Yeah, we agree that let's check for acceleration.

[00:51:23]>> Why? Let's verify it.

[00:51:38]Yes.

[00:51:42]I have not picked but let's hear let's hear >> like the second one we talk about as quantity and the last one that a body may beated even >> no that >> that is false >> that one that is true they didn't say anything about it that question statement that's speedometer >> that statement three Okay, >> it's actually true, but I'm still looking for a way to >> Yeah, three is true. Two is also true, but I'm looking for a way to get that acceleration stop. Very well.

[00:52:32]>> Okay.

[00:52:39]Do you have another question? Please question.

[00:52:53]What did you say?

[00:52:56]>> Yeah. Yeah. Yeah.

[00:53:08]You don't >> you question.

[00:53:24]>> Which of the following statements is true?

[00:53:29]>> About what?

[00:53:30]>> The first one. All quantities in mechanic are derived from the condition of three or four.

[00:53:38]>> Three or four.

[00:53:39]>> Yes, >> I know. It's only derived from two.

[00:53:44]>> All quantity all quantities making are from three or four.

[00:53:50]>> It's wrong because not not all four is not it's just three mass and time. So it's wrong.

[00:53:58]>> Statement is true. The second one is dimensional dimensional dimensionless physical quantities do not have units.

[00:54:09]It's wrong because you have some quantity that have unit but they don't have dimension like rad but they don't have dimension.

[00:54:18]>> So two is also wrong.

[00:54:20]>> The third one the dimension of a physical quantity is same as measurements.

[00:54:25]>> That's also wrong. The fourth one dimension is not same as unit. So that's >> fourth one regardless of the unit for a physical quantity the dimension of the physical quantity do not change.

[00:54:38]>> Yeah. Regardless of the unit since the unit is valid the dimension doesn't change. For instance acceleration is m/s square. Acceleration is also um >> new per kg. I hope we know. So whether so either of these units for acceleration the dimension still remain four only. Is that the answer?

[00:55:10]>> Yes sir.

[00:55:11]>> All right.

[00:55:14]>> Another one.

[00:55:16]>> Which of the following statement is or correct?

[00:55:21]>> A dimensionally correct equation may be physically correct.

[00:55:27]question.

[00:55:30]I mean I know you have question I know you have question >> I know I know question let's just have it >> a dimensionally a dimensionally correct equation physically correct >> a dimensionally correct the way the question itself like just thinking like a dimensionally correct physically correct >> that is dimensionally correct physically correct or even dimension is used to verify equations >> like since we are referring to equation like all those equation Newton and everything in fact for us to know that an equation is correct we use dimension to verify it so if dimension has verified that it's correct correct then there should not be condition again that may it should be surely be correct so that's that's like false but it's not it shouldn't be conditional another one >> statement the dimension of a derived quantity is never zero in any quantity >> dimension is never zero even dimensionless quantity doesn't have dimension of zero they have dime of one >> that's false >> it's false >> a base quantity cannot not be represented dimensionally in terms of the rest of the base quantities.

[00:57:13]>> I get I get that question. A base like a fundamental quantity cannot be represented dimensionally.

[00:57:20]>> That's true.

[00:57:21]>> Yes.

[00:57:22]>> I can't represent mass as length. Do we get a fundamental quantity can be represented dimensionally in times of the rest of the fundamental? That's true. So that's true. The dimension of the base quantity is zero inh >> the dimension of the base quantity is zero in any other base.

[00:57:47]>> The dimension >> the dimension of a base is zero in any other base.

[00:57:54]>> Yeah, that's true. three and four but let me check that very well.

[00:58:00]>> No, it's dimension cannot be zero.

[00:58:05]>> So the answer is three only.

[00:58:09]>> Okay.

[00:58:12]>> Quantity without unit has no meaning.

[00:58:14]>> No, it's false. It should be incomplete.

[00:58:18]So three only. Is that what >> Which one is correct?

[00:58:30]>> The first option said 1 2 and three. 1 3 and four. Three and four.

[00:58:37]1 2 3 and four. Then three and five.

[00:58:41]>> Okay. What is that five again?

[00:58:44]A physical quantity without unit has no number five is wrong. Is there anyone attached to three? Three and again that >> one two and three >> one and two obviously kilo and one >> a dimensionally correct equationally correct.

[00:59:04]>> Okay, let's just assume correct. What was two?

[00:59:07]>> The dimension of a derived quantity is never zero in any quantity.

[00:59:13]Yeah, it's true. Now we said is true.

[00:59:15]Then that means three is also correct.

[00:59:17]>> What of three?

[00:59:19]>> Three a base quantity cannot be represented.

[00:59:23]>> Three is also correct. So that mean that may number one they count it as correct then so one two and three just like that should not be conditional. Use dimension to verify an equation automatically the equation should be correct. Also this guy question I quantities are based on three.

[00:59:46]>> Yeah.

[00:59:47]>> No according to the slide understand but looks condition >> like when they say three and four like we should have said that is correct >> three.

[01:00:04]We already said that that statement is wrong.

[01:00:09]It's just theory. It's not conditional like specific is theory. So it's not it can never before. It's just theory. Even the way your slide put it is that let me say our okay your slide not our slide.

[01:00:26]is that all physical quantity under mechanics like all mass less than time like they dimensionally related to mass less than time just in fact they pass question just three in fact they also put three only and still correct what's now 250 So let's move on, shall we?

[01:01:04]Somebody's home, shall we?

[01:01:08]Let's do more on dimension.

[01:01:11]There is a question.

[01:01:14]There's a question.

[01:01:17]Can I remember this question?

[01:01:26]>> The one I did first test I'm trying to I think number four that is related to dimension.

[01:01:33]Why do >> we have any question? Any question?

[01:01:39]Yeah. Let's just shape.

[01:01:45]is given by x = y= >> find of a and dh and constant. So let's find of a b and since x and y are b >> obviously a square is also what a = >> lusen so dtq = l y so = ltus So the correct answer is LTUS 2 L the arrangement is important they ask you so you see some option they be the same but the arrangement will be passed very important any other question >> I'm thinking of entering very Given that >> given that capital letter >> Yes.

[01:03:45]Let's check this. So here we have E = <unk>2.

[01:03:51]Okay, now we have to remove the root first, right? By squaring both sides. So this becomes E²= 2.

[01:04:03]>> D of E.

[01:04:16]So that is still E = <unk>2 E = 1 /<unk>T are together <unk>2 has a dimension of 1 E = what? 1 / t 1 / 2 = t^ - 1.

[01:04:45]Is that the answer?

[01:04:49]>> No options.

[01:04:56]>> I'm just trying to answer. Don't if you square both you still return the square back because you are looking for not e^us.

[01:05:20]>> Yeah. Yeah. Actually just to be mathematically valid as well dimension violated some violates some law in math rather.

[01:05:44]I'm thinking of dimension dimension.

[01:05:57]Okay.

[01:06:09]Hello. Are we there?

[01:06:18]Are we there?

[01:06:22]You just sh active but this guy don't d this boy.

[01:06:44]I think there I want to do this dimension very well because people are not I'm trying to Reme where K is a constant.

[01:07:40]Is it KT or KX?

[01:07:45]WT minus KX. I progressive wave function formula.

[01:07:50]Yeah. WT minus KX WT minus KX YTUS KX.

[01:08:01]Find the dimension of direction.

[01:08:34]>> Okay. If W if W is the question, keep YT minus K If w it's not possible. I just want to say it. W is in kg. No, it's not kg.

[01:09:01]Actually, if in kg, what is the dimension for k?

[01:09:06]>> What is the dimension for k?

[01:09:10]>> It's in kg. What is the dimension for K and direction for A? A and K. What is the dimension?

[01:09:26]>> And Y is what?

[01:09:27]>> Where Y is in >> what direction for A >> and K where W is in Kg >> and Y is in meters.

[01:09:40]>> Oh. T X X displacement already. X and Y they are in T is in time.

[01:09:50]>> Wait in K and A.

[01:09:57]W KG Y X T is >> what do we get? K is in L.

[01:10:13]>> Yes.

[01:10:14]>> K is Mus.

[01:10:39]Whenever you have whatever you have inside a trigonometric function whatever you have no matter how it is or the dimension is always equal to what one.

[01:10:51]So all these guys inside function signs whatever you have inside function has a dimension of one >> and together with the trick function also has dimension of one sign everything has dimension of one and everything has dimension of one. The inside of function equals to one as dimension and together itself.

[01:11:16]So you can say wt= >> kx right?

[01:11:20]>> Yes. So W since W is in KG MT equals to what K= what ML - C.

[01:11:32]So this is correct. Are we together?

[01:11:35]>> What of A?

[01:11:37]So here we have y = a * that y = a and that's whatever is here whether or not multiplying a everything is just okay okay you can't conclude like that a is n because everything is one you can't a so we have so y= then y A also is what is a meter. You know why you can't a we don't have here we just have WT minus Kx can't say A is L though it's everything here that is equal to L everything together since so everything is equal to L. So it could be that a here is some maybe um tus 2 where all this one together is L t². Do you get? So you can't just a because everything here becomes one. So a * 1. I hope it's clear.

[01:12:50]So that's that for that.

[01:13:13]So let's move to vector tire vector analysis.

[01:13:32]efforts to open the slide. Let's just let's first do that first question.

[01:13:51]>> So is it?

[01:13:53]>> Yeah.

[01:13:58]>> 102.

[01:14:00]No, it's 102 before before they turn it to 101.

[01:14:06]a lady then during before you guys she did not attend my class. just like okay this time like I said broadcast I'm not doing it farmer I think let's continue.

[01:14:54]It's actually man that turned everything upside down.

[01:15:05]Are we how many of us know that vector has both magnitude and direction?

[01:15:18]Question. Can anything exist? Can anything exist without um magnitude for direction only? No.

[01:15:35]Are you sure?

[01:15:37]>> What about a unit vector?

[01:15:42]>> Does a unit vector have magnitude or not?

[01:15:49]>> What's the magnitude of a unit vector?

[01:15:52]>> One unit. So it no can exist without magnitude actually. Are we together? No, even if it's just a dot no exist without magnitude I was I remember something that so let's do that second semester shall we from here.

[01:16:33]A boy starting with a boy.

[01:16:38]>> Two boys.

[01:16:40]>> Two boys.

[01:16:41]>> Okay. Two boys. Ah, don't mind me.

[01:16:45]>> 10 new and 15 new.

[01:16:47]>> F1 = 10 Newton.

[01:16:50]F= what? 15 incline at 60° to each other.

[01:16:57]>> Incline at 60° to each other.

[01:17:00]>> Find the resultant in magnitude and direction.

[01:17:04]>> Find their in magnitude and direction of 10 15 they at 60° to each other. So we have to find the resultant.

[01:17:24]Are we together? Remember the sign rule r² = a² + b² - 2 a cos a minus theta.

[01:17:37]>> Are we together? But I prefer you always a square.

[01:17:47]They are the same. Are we together? So you don't need to be stressing yourself with this.

[01:17:53]So cosine rule is the one that you don't need. Just use plus I use the given to you. So here now we have r² = 10² + 15 2 + 2 * 10 * 15 cos 60. So we have 100 + what?

[01:18:14]>> 225.

[01:18:16]225 >> plus 300 * 0.5 are we?

[01:18:22]>> Yes.

[01:18:23]>> So we have 325 >> 300 * 0.5 >> r² = So r² = what >> 475 r = root 475 and that's what >> 8 new that's 21.8 new. Now that's our magnitude.

[01:18:46]That's magnitude of resultant.

[01:18:49]What of the direction? You can have two answer for your direction.

[01:18:52]>> Yes or yes?

[01:18:54]>> Yes.

[01:18:55]>> Consider your direction is in the 10 force is to >> the 15. Now let's divide this into two.

[01:19:07]>> Let's call this the one. Let's call this what the 60°. Now let's find the one.

[01:19:14]Bringing out that triangle triangle know this 15 is equal to this place.

[01:19:29]Two sides are par 15.

[01:19:33]So here we have you find this place you get what are the opposite angle of a parallelogram they are equal. This guy is also what 120.

[01:19:46]Are we together?

[01:19:48]Then we need sign. Um this side have angle theta 1 which you are looking for and this angle have 21.8.

[01:20:02]Are we together? No. Our horizontal is 21.8.

[01:20:06]We have angle 120 facing it.

[01:20:10]H >> say how do we get it 180us theta is 60° the original question we get and opposite angle of paralle 120 66 the total angle is 360° 60 + 60 get 360 so these are resultant so let's say 21.8 / 120 equals to theta is the angle facing this side. So we have 15 what theta I use at the bottom I use it cross multiply. So here you have 21.81 = what 15 sorry sine 21.8 8 sin theta = 15 sin 120.

[01:21:14]So here we have sin theta = what sin >> there.8 Hey, what do we get?

[01:21:43]>> What do we get?

[01:21:46]>> 30 should be 30.

[01:21:53]Now if you get this guy, you don't need to be looking for two by using sign rule again. Just subract it from 60 since the total angle there is 60. Now whatever we get is the is the direction of the resultant to the 10 force.

[01:22:10]Whatever we get as direction of the resultant to the what to the 15 force. Do we get that?

[01:22:23]>> We get this because of the 10 force and you don't need to use to stress yourself. Just subtract this from 60 to whatever you get to 15.

[01:22:38]So you can be your answer 10 for you have different value for the direction.

[01:22:45]The only time you can just divide 60 by two is if those two forces are equal.

[01:22:53]Those two forces are equal. Are we together?

[01:22:58]There is um Should we continue?

[01:23:09]>> Should we continue?

[01:23:13]Should we continue?

[01:23:16]I don't even want us to continue.

[01:23:27]>> How many people want us to continue?

[01:23:35]>> How many people want us to continue?

[01:23:42]How many people want us to continue?

[01:23:51]>> How many How many people?

[01:24:03]>> How many people want us to stop?

[01:24:07]>> You don't even know where you belong.

[01:24:19]So this already next question >> that I will be resing to horizontal and vertical let's do one of it even if you want to call it let's do >> okay If >> if three forces >> Yeah.

[01:24:43]If three forces f_sub_1 >> if three forces f_sub_1 >> let's pay attention >> is equal to 20 newton >> 30° northeast >> f_sub_2 50 new along west 40 new 50° northwest acting on a body.

[01:25:16]>> Act on a body. Find the resultant in magnitude >> and direction for F1 20 Newton northeast. Whenever I say northeast, it means the angle is coming from where?

[01:25:31]>> North. And northeast can also be set to be what?

[01:25:38]>> East of north. East of north is same as north east. North of east same thing as east north. South of west is same as west south. West of south is same as south west. Are we together? So whether east of north or northeast the angle is coming from what? North. So this when it gets to 30° 30° are we together? Yes. The first to this part which is 90.

[01:26:14]So we need part of the on the horizontalis and part that is on. Do we get what I did?

[01:26:21]>> Yes.

[01:26:23]>> So part of it that is fx horizontal and f_sub_y vertical. Now this I was there right and our angle is 30°. So fs we use sign because it's horizontal.

[01:26:39]There's no worry about that f(x) here is facing the angle. We want to find f(x) since it's facing the angle is opposite to the angle. So we f_y is adjacent to the angle we using car. Are we together? So f(x) I mean sorry sin theta = opposite what's opposite fx isn't it? cross multiply f(x) = what 20 s what >> 30 and the fact that on the horizontal fx is horizontal so that's i and it's positive now fy is adjacent cos theta what f_sub_y so f_sub_y 20 cos what 30 it's on the y a that's what j so our f_sub_1 = to fx X rather sorry our F_sub_1 rather equals to F_sub_X + F_sub_Y which is 20 sin 30 I plus what? 20 sin what?

[01:27:48]>> 20 what?

[01:27:49]>> 30 J.

[01:27:52]Are we together?

[01:27:54]Now for F_sub_2 F =50 J. How do I know? along west not north southwest west in this west and that's I rather >> I negative x ais which is negative i ais are we together now for f_sub_3 f_sub_3 = to f_sub_x plus f_sub_y what's our fx we told that f_sub_3 is 40 new 50° northwest northwest 40 new 40. Yeah. Are we together?

[01:28:34]>> Sorry. 14 50°.

[01:28:39]Let me draw it. Let me draw it very well.

[01:28:58]Are we together? 40 50° northwest.

[01:29:02]So it's coming from north it's going to west the angle. So when the angle reach here these are 50° the 40 new force is always there. So let's find our fx.

[01:29:15]So sin 50° = opposite fx 40. We cross multiply we going to have what?

[01:29:25]40 sin 50 as our so we have 40 sin 50 I is it negative or positive >> negative so we have minus 4 here what of our J our J will be what >> positive 40 what J so punch calculator let's punch next let's punch f= 30.5 that's 10 I isn't it?

[01:29:58]Plus >> 10 roo<unk>3 10 <unk>3 J.

[01:30:09]Yeah, it's terrifus F_sub_3. What is F_sub_3?

[01:30:35]What is - 40 sin 50us 304 74 something 40 25.

[01:31:00]>> Okay, the addition we have 25 what?

[01:31:04]>> 7 >> J. Let's add all the I together. 10 I + - 50 I - 40 I plus this.4 >> our F total 70.64 6.

[01:31:20]>> What of the J 10 roo<unk>3? What 10 roo<unk>3? Let's let's let's deal with it. 10 * <unk>3.

[01:31:28]What do we have?

[01:31:31]>> Plus 25.71 43 what?

[01:31:43]Let's find our famil 17.64 square + what?

[01:31:54]This 43 - 17.64 I + 43.03 J. Now our F total square root of -7 64 square plus what 3.03² 0 3² What do we have here?

[01:32:19]>> What do we have here?

[01:32:25]>> Take the root 80 something.

[01:32:41]82.71 >> Newton that's the magnitude of our resultant what of the direction use tan >> tan inverse tan inverse of what >> 14.03 don't bother about this minus 17.64 But we are going to use it to determine the quadrant. If you are not using quadrant is not in your answer, use the negative to give you another answer. It give you negative which must be your answer. But if you have quadrant, you don't need to add it. Just use the coefficient alone.

[01:33:20]The magnitude alone rather. So we'll be using the negative to get the quadant.

[01:33:26]So this over this and take the time inverse. What's our t 31.74°.

[01:33:36]Now let's check which quadrant >> 31.34°.

[01:33:42]Now let's check which quadrant our the addition of our the total force our J is positive J is positive.

[01:33:52]What's our X? Negative. That's where >> 7.34° on the second quadrant to what? To the negative x ais.

[01:34:05]Second quadrant to the negative x ais.

[01:34:07]What am I? Second quadrant to the x ais.

[01:34:11]Don't need to put negative. The negative is y is on the second quadant. To x just saying like to the horizontal axis.

[01:34:19]31.34° on the second quadant. to the x ais to the horizontal axis. I hope it's clear time now.

[01:34:31]>> So let's just call it >> so we do trusting go we do more when others will come tonight. So some are not around because of the co and prepare for your co.

[01:34:54]>> Thanks.

[01:34:57]Hello guys, you are done.

[01:35:02]So all right, good night. I will upload the two videos. So guys, you can watch later. All right, bye. Take care.