How can I solve physics without a calculator? If you want to improve your time, speed, efficiency, and marks in physics, then this video is for you. Assalamu Alaikum Champs!
I am Usva and in this video I will tell you some tips and hacks that will be a treat for you after seeing the numericals that you find challenging. So, watch this video till the end. Keep in mind that if the examiner is giving you a question to solve without a calculator, then it is obvious that he will always give you such values that you can easily tackle.
So first of all, let's start with indices. In MD-CAD, you have to encounter these most often. These are usually called pars. If you deal with them, half of your questions will be solved here.
First, let's see if we have a number x and its par is x. a is multiplying with another number x and its power is b. So when two numbers are multiplying, they will multiply as it is. For example, x multiplied by x, whatever number comes, let's say x comes.
But the powers that will be a and b, these numbers will multiply but the powers are going to add up. So what we will do is write a plus b. Okay, so this is the multiplication rule.
But if we have a number x, whose power is a, and it is being divided by a number x, whose power is b. So now what do we have to do with the powers? What's going to happen is, you will divide x by x, whatever number you have, that will come, write a. Now the rule is, when they are being divided, the lower power will go up, and its sign will be inverse. If b has a positive sign, it will go up and become negative.
If it has a negative sign, it will go up and become positive. Since it is positive, when it goes up, it becomes negative. So, a minus b will be a. These are our two basic things. Then, suppose you have x given, its power is 2, then there is a bracket, and then another power is given, for example, 3. Okay?
So now these parts will not add up, they will multiply. So x raised to the power, what will you get? Two 3's are 6. So the answer would be x raised to the power 6. So we have 3 rules here.
Let's look at the fourth one. If x is, its power is 1 by 2. What does this mean? The second representation of this could be that it's written like x, and here it's 2. Usually, this 2 is not written.
So whenever you see under root x, under root means 1 by 2. But, if there is another number, instead of 2, it will be 3. For example, x raised to the power 1 by 3. So here, 3 is written, so you know that it is 3. If there is no number given, then it is 2. Then, if there is a square on this number, let's say, there is a square on this number, So, this 2 will be cancelled from this 2 and you will have x raised to power 1 which is also equal to x. Okay? So, if there is a square on the under root of this number, this square will be cancelled from the under root and you will have only x.
I hope you have understood. Now, let's come to another very important thing. Let's say we have x is 8. 8 into 10 raised to power... 4 and at one place 8 into 10 raised to power minus 4 so now there is a huge difference between these two this means that if there is a positive power you have always remember that positive power always means that whatever the relation is after this number always this side has its relation if it is negative then it will have its relation behind this number always remember okay Let's say if 8 into 10 raised to the power 4 is there, then it will be equals to 8 10 raised to the power 4 which means we add 4 zeros, 1, 2, 3 and 4. What happens in negative? 8 minus 4 is there.
When a number doesn't have a decimal, then its decimal is always at the end, here. The number that doesn't have a decimal, its decimal is at the end. So this decimal has to move 4 places backwards.
What will happen? 8, one number is done, one point is moved back, 1, 2, 3 and 4. So, these four decimal places are moved back and come here. So, this will be the representation of 8 into 10 raised to the power minus 4. Similarly, if you get a number, you convert it into 8x10 raised to power minus 4 or plus 4. I just told you that if the relation is after the number, it will always be positive on the right side. If the relation is on the left side, the power will always be negative.
Then the power will be positive. And on top of this, 8x10 raised to power minus 4. Why will it come? Because its relation was backwards from 8, it was on the left side. If you understand this, your numeric will be solved easily. And if you don't understand, you will make a lot of mistakes.
Now the next thing is standard units and prefixes. You should know these on your fingertips. If you know the standard units, you will convert them. Because whenever you want to solve a problem, you have to convert it into a standard unit.
For example, there is a meter for length. What is weight? I will display this chart on the screen You can see it properly These are the charts in the first chapter of your Physics You can memorize them properly Suppose you are given a wavelength in a question For 20 nanometers Now, if you solve it like this, the answer will be completely different First of all, you have to convert it into the standard unit That is meters So if you know which one to convert to nano, then you can solve it.
So 420 into 10 raised to the power minus 9 meters. This is the value that you will get when you put it in the formula. Now let's solve a small problem.
For example, you have 0.2 divided by 8 into 100. Now you will think how to solve this in 10 seconds without a calculator. It's very easy. First of all, we will convert 2 into scientific notation So we will get So 2x1 is 2x2 is 4x8 is cancelled 4x1 is 4, 4x4 is 4, 4x25 is 100 So we will get It is minus 1, which means it will go backwards So if you move the decimal from here to here, you'll get 2.5.
You can check the calculator and see if you get the answer. Let's talk about perfect squares. Usually, the perfect squares that you get in exams are So your task is to get from 1 to 20 on your fingertips.
If you get it, it won't take you long to solve it. Sometimes, you don't get a perfect square. You get a number that you have to assume is its perfect square.
Let's say, we use a thing in physics that is very useful to us. The value of pi is 3.14 and you get its square. So this is difficult to calculate. So we assume that the value of this is equal to g whose value is 9.8 and normally we consider it as 10. So g is always equal to 3.14 square.
Let's apply this in the question. So the question is there is a second pendulum. Second pendulum here, aapne uski We have to find the length. It's a very easy question. The time period of a second pendulum is always 2 seconds.
So we will put a formula, put its value and find it. So time is equal to 2 pi under root L over G. Okay. So, first we have to find the length.
So we have to separate the length from the under root. So for that, we will take a square on both sides. So this will be t square, this will be 4 pi square, and L over g will come because this square has cancelled it. I just explained it to you.
Here we have it, let's shift L to one side. Now here is our formula, we'll just put the values in it. What time did we have?
2 square into g, 9.8 divided by 4, 3.14 squared. So we just discussed that this will cancel because its square is equal to this. 2 x 2 is 4, so that will also cancel from 4. So the length that you get is 1 meter. And usually, when you find it with accuracy on the calculator, you get 99.3 cm, which is nearly equal to 1 meter. So, this way, you solve your questions with estimation.
Now, let's see where perfect squares are used. Let's take an example that you are given a distance of something, it traveled from here to here, it covered 3 meters, from here to here it covered 4 meters. He is asking you to find its displacement.
This is equal to question mark. Now how will you find this? You will apply Pythagoras theorem if you remember.
So, x squared which you have to find is equal to 3 squared plus 4 squared. x squared is equal to 33 is a 9 plus 4 is a 12. 16 sorry. And you add it, it becomes 25. Okay. So, Now to complete this square, we have to take the under root here and here as well.
This square will cancel it. And, first of all, you put the perfect squares here. Now you know the perfect square of this, so you know whose square is 25. It's 5. So x is equal to 5 meters. I'll tell you one rule in which we make a lot of mistakes.
It's a very simple statement, remember it. It's a very simple statement. Anything divided by 0. If you do this on a calculator, it's always going to give you an error.
Why does this mean an error? Because whenever a number is divided by 0, it's always equal to infinity. And whenever a number is divided by infinity, it's always equal to 0. So the statement is, anything divided by 0 is equal to infinity.
And anything divided by infinity is equal to 0. Now we come to a very essential thing. If you are an MD-CAD student, then you should know these values very well. What will happen?
Theta values. Which looks like they can't be solved without a calculator, but they can be solved very easily. Let's see.
We will label them. I will tell you a very easy way. Sin theta, cos theta, and tan theta. Now the common values that you get in exams are always these 0, 30, 45, 60, 90, 180 and 270 degrees Now a very simple thing that you have to remember is that the sin theta is the minimum at 0 As we go towards 90 degrees, it increases and the maximum reaches 90. But the cos is inverse.
Cos is maximum at 0 and minimum at 90. So as we reach 0, it becomes maximum and decreases as we go towards 90. If you keep this in mind, now we will solve it. First of all, sin 0 is 0 because it is the minimum value. sin 30 will increase towards 90. So, this value will be 1 by 2. 45 is 1 by under root 2. 60 is under root 3 by 2. You have memorized this part.
After that, 90 is the maximum value. When the maximum value is there, you write 1. So, sin 90 is equal to 1. sin 180 0 is inversed. So 0 is inversed by 0 of course.
Okay, 270. This will be 90 and minus 1 will be here. Then cos theta. Cos 0 maximum 1. Now this is written from here to here, we have to inverse it. 30 will be under root 3 by 2. 45 will be 1 by root 2, same value.
And 60 will be this value, 1 by 2. 90. It becomes minimum. Okay, 0 is here. cos 180 inverse of 0. So what was this?
cos 0 is equal to 1. So its inverse will be minus 1. And if the inverse of 270 is 90, then here 0 is here. Okay? Okay.
Now tan theta is the value of its equal sign over cos. So 0 divided by 1 is equal to 0. Is it? Yes. So then we have is 1 by 2 divided by under root 3 by 2. You will solve it. 2, 2 will get cancelled.
You will have 1 by under root 3. Let's check 45. 1 by under root 2, 1 by under root 2. Both will get cancelled. You will have 1. 60. So tan 60. We will solve them. 2 by 2 will get cancelled.
Under root 3 will remain. Then in 90, 1 divided by 0. I just told you the rule. Anything divided by 0 is equal to infinity. Very good. So 180. Tan 0 divided by 1 again.
Now it's divided by 1, so it's 0. The negative of 0 is not positive, so it's 0. 270, its inverse, so infinity. Very easy table. You draw it, revise it daily, and you'll easily remember the amount you revise.
Now let's solve a question and see how to apply it. Also, in every question, you don't write these values in such a way that you have to put their solved value somewhere. For example, 1 by 2 equals 0.5k. 1 by under root 2 equals 0.7k. Under root 3 by 2 equals 0.86.
You have to remember these. These three values will be the same as these. So, 1 by under root 3 equals 0.57. Under root 3 equals 1.7.
So you have to remember this too. You may find it difficult, but it's a two-month practice. That's why physics says that the more you practice, the more you will remember things. Now let's solve one question and see how we can apply these values. Let's say you have a question, a figure given.
In that, you have initial velocity, acceleration, and time given. You have to find the final velocity. Let's put the values.
You have to find Vf, you have to write as it is. initial velocity is 10 meters per second plus acceleration is tan 60 now we have to solve this and time is 10 seconds lets do this tan plus now tan 60 is the value of under root 3 multiplied by 10 now tan plus, what is the value of under root 3? 1.7 multiply by 10 so let's solve this if you know multiplication then that's very easy this is zero because of this point will come forward so it will be 17 so the answer will be 27. the velocity is of course meters per second that's how we solve such kind of questions so now i have explained to you all the basic rules now it's your turn to solve this question mass is given, velocity is given, you have to find the wavelength I have also told you the formula, in this a constant is being used, Planck's constant I have also told you the value of that, 6.63 into 10 raised to the power minus 34 now all you have to do is to put these values in this formula and solve it with that calculator, and then pause the video solve it, tell your answer in the comment section, then we will resume and solve it So we have solved our question and now let's see if the answer was correct or not We are putting the values in this formula, we have applied H as it is We will not apply mass as it is because it is given in grams How will we convert this into kgs? We will divide 200 by 1000 and you will get 0.2 kgs So here we have to put 0.2 Multiply it with 330 now the next step is going to be that you have to finish the decimal places if we write it like this 6.6 into 10 raised to power minus 34 now this decimal point is going to move one point forward but from here we move it one point backward to finish the zero point so what will happen is that we will have 2 into 10 raised to power minus 1 and here 33 into 10 raised to power plus 1 So, we will cancel this one.
Next step is 2, 1s are 2, 2 3s are 6, 0.2 3s are 6. So, you have 3.3. Let's finish the decimal, let's make it 33, into 10 raised to power. Since the decimal will jump here, then minus 1 will come. 10 raised to power minus 34 will come.
Below, 33 as it is will come. It will be cancelled. Now, minus 1 minus 34 both will add up sign of the bigger number minus will come so your answer will be 10 raised to power minus 35 that is the wavelength of this question Wavelength and meter will be attached to its unit.
That's all for this video. Thank you very much for watching till the end. If you liked this video, then do like it. If we hit 1000 likes on this one, I'll surely bring a part 2 for you.
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