 This too solid question like this is good red rather than giving you shades All of you getting see see you have to be very honest with yourself if you are not getting it you have to say that I am not getting it otherwise you will time to just go all of you got it. This means yes or no and this this also means yes this also means yes strange or it matters with what frequency you are. Because Indians they hate to say no for anything so they will be like from there inside no is coming out so it will be like yes. Anyway you are American citizen right Bush. Kinetic energy needed to project a body of mass m from the earth surface to infinity. Is this escape velocity under root 2g Re so half m into 2g Re so mg Re. Okay then this one particle at rest distance r above the earth surface a minute speed it is again the escape velocity only but here in this chapter you keep on using this formula again and again. Okay u1 is u2 is 0 stop talking k2 is 0 why k2 is 0 because you are trying to find a minimum initial velocity this is gmm by 2r so earlier it was just thrown from the surface of the earth because distance from the center was r now distance from the center is 2r so that is why u1 is this. Okay so root gm by r it was root gm by 2r like 2gm by r root 2gm by r the last objective question after that subject will start. No sir you will be saying we will not be here. No. A is not correct so A is out we just have 3 options to choose so a chance that you will get it right is 1 by 3 now. Done even C is wrong then why is it wrong even B is wrong answer is D what is asked relative velocity is asked connecting energy depends on absolute velocity. So relative velocity if you are throwing with respect to satellite like this this is your relative velocity absolute velocity will be v and if satellite velocity is u the absolute velocity will be v plus u but it is v minus u. No v plus u relative to this is like that v plus u and if it is like that relatively then v minus u. So it depends right connecting energy depends but if it talks about the absolute velocity then does not depend. So I think 30% question you did not get right 2 subjective questions we are starting with the simple basic ones both of them. Let us do one by one the first question you have 3 minutes to complete. Another mass is kept over here the force on this mass because of these two together will be 0 cancel out the only force will be because of that so net net force will be upward this distance is how much? Rho 3 a by 2 so distance between these two is Rho 3 a by 2 these two forces and you are getting cancelled. So net net force is g m square divided by Rho 3 a by 2 whole square right this is the answer what about the midpoint or the centre of triangle is centroid. Here it will be 0 you can see that one force is here other force is there this one is here they are they are in equilibrium how do you know? This angle is 120 this is also 120 this is also 120 if they follow the sign rule then they are in equilibrium what is the sign rule? Suppose is alpha beta gamma f1 f2 f3 if f1 by sin alpha is equal to f2 by sin beta beta if this is true then they are in equilibrium you can also check on x axis and y axis net force both will come out to be 0. Land is theorem we have done it right vectors okay this one second one Rho 3 g m square by 4 g m square by 4 g m square by 4 g m square by 4 g m square by 4. 3 uniform spheres are captain such as Rho 2 so I think this is also simple only you just have to get the diagram proper this is between these two is 2 R between these two also 2 R since they are sphere I can treat them like point masses located at the centre okay. So this is one force this is another force you have to find the magnitude of force any one of the sphere due to the other two. So there are two forces both are having magnitude g m square by radius square this is f1 and this is f2 also. So two forces applied at an angle of 60 if you form an equilateral angle or not right. So two forces are at 60 degrees so net force will be root over f square plus f square plus 2 f square cos 60 which is equal to root 3 f so root 3 times this is the answer done. See if you are not getting the first one you can try out the second one also. Someone is talking about dancing stars right here you have four masses dancing around. How they will move? How they will move? They will move due to their own mutual gravitational attraction and it should be symmetrical motion because everyone will move in a similar way okay. Only option left is with respect to this axis all of them revolve around like that I am getting it. So they will move in a circle of this all these four masses this is how they will move and all of their velocities will be same and every movement they will be forming a square only. Now solve it the answer is little weird 2 root 2 plus 1 divided by 4 under root of that into root of j m by r. See the net force on this you have to find out it will be towards the center one force will be from this mass one force will be due to that mass. So net force in this direction will be cancelled away getting it and net force will be in that direction. So that net force is equal to m v square by r where r is what you can find out r using the v square shall I do it? Along the circle radius is r only which is given. What third mass? Third mass has to attract it right. Yeah it is attracting. You said the one gather say. Yeah it is attracting. Yeah that is with the components. They are attracting now. Suppose this is 45 degrees this is f1 this is f this is f. So 2f cos 45 plus f1 this is the net force which is equal to mv square by r. Any doubt here? The force towards the center is mv square by r. Okay f is equal to gm square by this distance how much is this distance? This is r. This is r by root 2 so root 2r root 2r whole square this is f f1 is what? gm square divided by how much is from here to here this is root 2r this is root 2r this is equal to 2r. This 2r right? Okay so 2r whole square substitute f1 here f here you get the value of velocity okay. Yeah this question was one of its kinds okay sometime they will tell you that there is an equal to triangle they start they started moving due to their own gravitational attraction so from the centroid they will move the center of mass should be at rest because it is internal force right. So center of mass should be at rest and they should move the only way possible is that they move in a circle like that so that center of mass is at rest okay. So then you find out the net force towards the center gravitational force net gravitational force towards the center and equate it to mv square by r because it is a circular path. So why can't we do that thing that like remember we had that question in which we all come towards the center why won't it do that? No it will still be at the center. The center of mass position won't change but the gravitational potential energy will change right but yes the loss will change the kinetic energy will also change but then the coming to them. This they can come towards each other but this clearly written here that they are not they have enough velocity to sustain this radius you have to find that velocity but if they don't have enough velocity to sustain this radius so that they are able to sustain that. Black holes came close to each other like what he was saying last class they started dancing because the velocity in tangential direction is attained so much so that it can move in a circle of that small radius. Same thing I am not getting into calculations ok we have so many questions this is how you have to solve it and the final answer I will just write down ok. Final answer is root over gm by r this this one now second one it's all about calculations the next question So get the calculation right there is nothing else I know the concept but I am not making serious that's the most stupidest thing. In jr means you are not getting calculator remember that 0.661 yeah not getting it 0.6 say how weak we are in calculations if they don't do the hand calculations usually. Sir I got 0.6 they don't calculate up to that point. What did I get 0.65 Yeah 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 0.65 Yes sir I got 65 by 100 I have approximated a lot 74 is approximately 77. Anyways so the expression due to gravity you have to find out so gravitational force divided by mass that is the expression due to gravity ok. Gravitational force is gm mass of moon divided by radius of moon plus height this is the gravitational force this is equal to m into g. So g is this ok and if you want to take a risk you can say that g is equal to g at the moon surface is g0 by 6 into 1 plus h by radius of moon the whole square. You can translate the same formula if you have derived for the earth but the values might be given such that it may not come out to be g0 by 6 ok. But if you already have a prior knowledge that actually due to gravity on moon surface is g0 by 6 1 6 of the earth ok. Then you can take a risk like this understood ok. So it will get 0.65 roughly.