Simple Pendulum in an Accelerating Car/NLM/11th/NEET/JEE/Pseudo Force

Added: 2026-05-26

[00:00:01]Hello dear students, this is Iklager.

[00:00:04]Uh so my dear students, today I am going to discuss one of the beautiful problems in Newton's laws of motion and that is simple pendulum in an accelerating car.

[00:00:18]Right? So it is like this simple pendulum inside an accelerating car.

[00:00:22]Okay? And in this question what we are supposed to calculate is that we have to calculate the angle that the string makes with the vertical. And number second is that we have to calculate what is the tension the string. Okay. The problem looks like this.

[00:00:47]Simple pendulum. This car is accelerating towards right. Simple pendulum. It will it will deviate back.

[00:00:55]It will go like this. Okay. And it will make some angle theta with the vertical which we have to calculate. And number second we have to calculate tension the string. Okay. The first thing you will tell me is that how many force are there on this bob or on this ball is ball percember one is that in the vertically downward direction there will be mg which is weight. This one number second is that number second is that the tension string along the length of the string and number third is that there is the speed of force as well of force this one FP equal m into A. The reason is that observer nonertial frame of reference. Okay. So how many force are there? There are three different forces acting on this ball. The next thing I will do is I will construct a free body diagram. I'll construct a free body diagram. Okay. In this y-axis and this is x-axis. And here we have this is a ball whose mass is equal to m a. Okay. Now how many force are there on this ball? One force in the vertically down direction is m into g.

[00:02:04]Another force in this direction is pseudo force which is m into a. And one more forces along this direction which is tension in the string makes an angle of theta with the vertical. All right.

[00:02:29]E sin theta. Okay. So there are two components of this tension the string. G to next.

[00:02:39]Now the net force is equal to zero. Net force equal z. It means that this t sin theta will be equal to m* a. And the upward force which is t cos will be equal downward force which is equal to m * g. So this t sin theta is equal to m into a. And this t cost co will be equal this m * g isn't it? Okay. So let me write down those two equations. So the equation number first equation of first will be that is t sin theta comes out to be what? It comes out to be m into a and the next equation is what? That is t cos theta comes out to be m * g. Okay. So here we have these two equations. This is our equation number first and this is our equation number second. Okay. Now in order to calculate in order to calculate the tension string sorry the angle which the string makes the vertical I will divide these two equations. I will write down first equation divided by second equation equations divide. This t and t will cancel sin theta cos tan theta or m cancel a / g. Okay.

[00:03:56]to theta theta comes out to be tan inverse of all this that is a divided by g. So this is our important result the angle which the string makes with the vertical very very important result. Okay. So number one number one number one is this G number second is that number second is that number second that we are supposed to calculate the tension string m a mgle sir that is 90°. If it is 90 if it is 90 tell me one thing can we calculate the net force of this mg? Yes of course we can calculate that. That will be obviously equal to that will be obviously equal to square root of this square plus this square. So that will be in turn equal to tension. So that means the tension will be equal to something like this. It will be something like this. It will be square root of m a square plus mg square isn't it? Okay. So we are we are done with the tension as well. So we have calculated both the things that is we have calculated the tension string and we have calculated the angle that the string makes with the vertical and I have done one thing and that is I have highlighted both these results for you. Okay. So see you next time with one more important problem in NLM.