 Alright guys so today we are doing problem practice on the gravitation chapter so as you can see we are we have already started and here are the first two questions I have taken it from a well-known source which you will find out if you do enough problem practice anyway since you haven't done it you will not able to know right now start solving it you have four minutes to complete these two questions so the first answer is B for Bombay and second one second one is C okay all of you understood or should I discuss I will quickly discuss expression of moon with respect to earth is given right so the force between earth and moon will be expression of moon is given which is what V square by R only second literal expression okay so suppose this is earth and that is moon so it's acceleration V square by R is given so the force between earth and moon is mass of moon into acceleration simple right mass of acceleration is force acceleration is that much so mass of moon into acceleration is the force now if it stops revolving then what will be the initial acceleration towards the earth so this was balancing this this this was balanced by the gravitational force now if velocity is becoming zero the gravitational force will still be this much only in magnitude okay this will be equal to mass of moon time the acceleration of moon when it is coming towards initially when it was revolving around the accession was because of the circular motion now when it stops the acceleration will be because of its movement towards the earth okay either it will have second literal expression from the same force or it will start moving towards the earth same force will be same so that is why excitation in magnitude is same excitation of the moon just before it strikes the earth how much why so the when when it hits the total distance will be okay so the radius of the moon is it given one fourth of the earth radius so this is the earth and stop talking there's a moon moon's radius is r by 4 so how much is the force on the moon right now mass times g effective okay and g effective for the center of mass of the moon is g0 1- 2h by r so 2 h by r if you use is it g0 by this is an approximate formula isn't it the exact formula is how much g0 divided by 1 plus h by r whole square so this is this is the g so here you put h is equal to r by 4 to get the exact g0 so here so here if you put what you get g as g0 by 16 by 25 g and here if you put this what you're getting it as g0 by 2 right so these are there's a big difference so you can use this because the height h is not very less compared to the radius of the earth okay simple question okay okay what is the answer for this one see suppose the accession due to gravity at the earth surface is this and the surface of Mars it is 4 okay why it is seen anyone there has to be some point where the net gravitational force of traction will become zero there should be and there should be only one point so it can't intersect at two points okay it can't work see negative is like which direction you take positive or negative so it can you can say negative also but definitely it can't have two points so then it also shouldn't change sign which should not change a sign as in now here the weight they are assuming it to be a magnitude of it okay but they can assume the width sign also that's what I'm saying that it can be negative also assuming what you're printing positive negative but definitely it can't have two points having zero gravity first one D for donkey how will you do the first one explain who are deep but I calculate the force on earth you get you know the M.E.M. by R.E. Swear then you calculate the force in that other planet writing stuff in terms of writing like the mass and the radius in terms of the earth's quantities so mass is twice how how are you I didn't continue okay so G M.E.M. by R.E. Swear what is this G M.E.M. by R.E. Swear what is this the force on earth the force on earth okay then then a force on the other planet is let him only speak is G into 2 M.E. 2 M.E. M by so if you do 4 by 3 by R.E. Swear you get the radius is radius and if I do 4 by 3 by R.E. Swear if you use volume and density to calculate the mass of this second planet okay so two times mass of this should be equal to density is how much is equal to the density of earth rho into 4 by 3 pi R.Q which we don't know yes okay and mass of earth is rho into 4 by 3 pi radius of earth Q okay you can divide it and yes this is what you get R is equal to 2 ratio power 1 by 3 times radius of earth this is what you got yes right the substitute here you get 2 ratio power 2 by 3 stop talking R.E. Swear right yes so is that what they're asking huh so 2 divided by 2 ratio power 2 by 3 is 2 ratio power 1 by 3 this is D okay so you can see that this is that much times of that yeah straightforward this one mdr by 2 others yeah how you solve this work done is equal to change in mechanical energy kinetic energy doesn't change initial activity is 0 final category also 0 slowly you're bringing it there okay so what was done is equal to final potential energy minus initial potential energy and how much is the final potential energy equal to you do equal to minus g mm by 2R earth surface is lifted up by R so from center it is 2R so you want is minus g mm by R so you get g mm by R this is equal to your work done sorry 2R and g m by R square is small g so this is equal to half mgr okay so problems like these come in j means done yes both smart we haven't done the second one do both questions answer for the first one see and for second one see I think second one is straight forward these correct is wrong the plot of V against R is actually continuous it remains constant till the radius and then it drops so it's a continuous graph whereas the field is zero and suddenly picks up and then it goes okay so see for this and here it is work what is it? So work done is u2 plus k2 so k2 is equal to half m1 into 2 square stop talking from infinity right so u1 is 0 and k1 is 0 and w is minus 3 so u2 is minus 5 so potential is minus 5 potential is mass into potential so mass is 1 so potential is equal to potential energy in front of you okay what's the next one so it is independent of mass how will you derive it mv square by R is equal to g m1 m2 by R square so from there you get velocity and 2 pi r divided by velocity is the time period you'll see that mass of satellite disappears it's independent of that okay have you seen the gravity movie? Debris was flowing in the same radius irrespective of their mass after some time it again and again comes back to the same point so what I didn't understand is the gravity was going to be faster than the no no no actually the thing is that the speed will be same your movie like this they are coming like that oh so they can't catch the speed is same velocity is in opposite directions but if you are there you can't change the direction of your own velocity you can't apply force on yourself these two so it can't be used negative it can't be it is a little magnitude you didn't take magnitude see in J in the exam like J they want you to make errors so they they will do every such thing possible so that you make silly errors it is not a game of knowing a lot of concept J means is about not making silly errors simple J means is about not making silly errors advances about knowing concept to the depth okay so you can't just do silly errors and laugh about it you just gone behind 12,000 ranks if you get this wrong okay it will hit you badly this one both are B yes it is also be anyone who did not get this it is capitalist law of areas so equal areas will be swept in equal time so that is why see almost every time we assume that whenever it is not given we'll assume that planets are moving in a circular path if it is elliptical it will be mentioned separately like this okay then you have to apply capitalist law these two no no no it's cna cna because it's moving in a radius so normal force is you normal swing balance is a normal sensing thing that is cna logic may or may not be correct so because like this the spring has no force acting on spring guys man it's a spring balance the spring has no force on where it is oh second when I was looking at the first one so answer is c and a so basically if you are revolving around the planet okay then you will feel the weightlessness the reason for that is that whatever is the force acting on you this direction on your frame suppose you are standing inside the satellite with respect to you a pseudo force will be acting on you which is mv square by r and there will be g m1 m2 by r2 both will be equal always it doesn't matter what if you sit in a chair you will not be able to generate an extra force extra normal force to feel your own weight what you feel is a normal force what humans are designed to feel only the force humans are not designed to feel anything else okay you're designed to feel change in velocity which is acceleration but you can't feel the absolute velocity okay and similarly you can't feel the anything else other than force so there is no force which you are feeling so you feel weightless because whatever is the force applied by gravity is balanced by this anyways this one a body is suspended from a spring balance the recording of balance is w1 when the satellite goes in orbit of radius r w2 so weightless both both are weightlessness so w1 will be equal to w2 it doesn't matter actually whatever the radius of revolutions it is weightless ring can't apply any force okay spring balance the weight is kx whatever the force spring applies that is what the spring will show as a weight