Std xi physics: Dimensional Analysis

[00:00:00]Hi students, how are you today?

[00:00:04]Hi students, how are you? Today I am going to post video for standard 11 first chapter measurements.

[00:00:15]The force acting on a body moving in a circular path depends on mass of the body m velocity v radius of the circular path r. obtain an expression for force by the method of dimension analysis.

[00:00:35]This is very very very important question and before that I would like to tell I have given separate link for how to derive dimension formula for various physical quantities. Please check my link. So let me come to the point. So first of all what they have given is force F is directly proportional to mass. So you have to assign one variable X and then velocity V for which we have assigned a variable Y and for radius R and similarly for is. So here they have given K value is given. Suppose if they have not given any k value you assume it one not to confuse they may give one more uh physical quantity such as theta pi mere number. So please ignore only these three fundamental three fundamental quantities only the physical quantity depends on. So you have to follow this format. This is the format we are supposed to follow.

[00:01:44]the format physical quantity and then dimension formula you have to put two columns and then whatever be the quantities they are given force capital F for which dimension formula is MLT minus 2 mass capital M velocity LT minus one radius capital L and then substituting this relevant dimension formula in the above expression so MLTUS 2 K^X LT -1 all ^ y L power EZ and then K M^ X L power Y T power - Y L power EZ and then what you are supposed to do is you have to compare the coefficients of powers in terms of M LT so what is the value of M here one so X is equal to 1 here y + is equal to 1 and here - y is equal to minus t for t time period. So minus minus get cancel. Therefore you got directly y value is two and here also you got directly x value is one.

[00:02:53]Let it be equation one. Let it be equation number two. Equation number three. So you are supposed to find isert. So substituting the value of y in two. So 2 + isert is equal to 1. Isert is equal to minus1. Okay. Let it be equation number four. So we have found three values and three variables x = 1, y = 2, isert is = minus1. Now we are going to substitute these variables values in this expression.

[00:03:26]See what is the expression we have given. KF is equal to k power x v power y r power. So whatever be the values we have found I have mentioned here x = 1 y = 2 isert is equal to minus1 k = 1. So f is equal to m^x 1 v 2 into r power - 1.

[00:03:51]What is the 1x x inverse is 1x no like that r - 1 is 1x r. So f is equal to mv² by r. So this is the formula for centripetal force that we'll be learning in uh upcoming chapters that is a third chapter and similarly in fifth chapter also rotation of motion also we'll discussing this formula. So F is equal to MV² by centripetal force the force which always acts toward the center of a circle that is what they asked to derive by the method of dimension analysis. How you can also verify whether your equation is dimensionally correct or not by using the method called what? Check the correctness.

[00:04:32]ML LT minus 2. What is the dimension of M? Already we have given in the table M velocity LT minus one. How many times? 2 * R L and then M L² TUS 2 L this will go to top L minus one. So how many L minus that is here? L² L - 1 L T -2 so MLT -2 ML T -2 so the above expression is dimensionally correct this above equation the expression is good for dimensionally correct for centrial force okay thank you this very very important five mark question so one more analysis method is there how to find the expression for time period of a second pendulum and that one and this one the mass general uh These two questions are very very important. So please go through this. Okay. Thank you and subscribe my channel subra money physics.blog.com.

[00:05:31]Thank you.

[00:05:34]Basic pattern.