if-the-speed-of-a-satellite-orbiting-the-earth-at-a-distance-r-from-the-center-of-the-earth-is-v-w-2

Question

If the speed of a satellite orbiting the Earth at a distance $r$ from the
center of the Earth is $v,$ what is the speed of a second satellite orbiting
the Earth at a distance 2$r$ from the center of the Earth?
(A) 2 $\mathrm{v}$
(B) $\sqrt{2} v$
(C) $\frac{1}{\sqrt{2}} v$
(D) $\frac{1}{2} v$

Salamat Ali · Accepted Answer

the speed of Is it light it the distance are, uh he&#x27;s given by these equal to the square root off rev additional constant times. The mass of the earth divided by the radius are so so it is proportion to the square root off our then, for the two are lost. It will be proportional Thio, you near for a new radius to our this will be initial. I lost two divided by so that we call it we if Do you mind? My skirt moved off to so option C is the right answer.

Ankit Gupta · Answer

we are given velocity function as Underwood one point before independence to the father 12 divided by. So we need to find velocities or the tools and the lights. This is Earth on these are located. I say this is a late one on. This is a delight to so the students offset late one is 100 miles an A steward&#x27;s 200 miles on our is given by values of Earth plus D distance and beyond. Given Raiders off hurt us 3950 lights. So this car bullet velocity one All right, this is equal to under load one point pulled independence to the power Well divided by three night by zero. Plus 100 It isn&#x27;t world will if I take else him down Build remained 1 24 into tenders to power 10 divided by or the roof bag zero National is a denominator My glamour or little by little Divide was, you know, a zero So we get inside 1 24 into 10 raisport pen into 4000 and 50 derided by 4000 and 50 So this is a will do 1 24 into 4040 Underwood will give me 708 0.6 in tow. Penry, Stober and half divided weapon was little finds little. This is equal to 10 days to people by my final answer given will be equal to 1749 by my is blood A look. Now that discovery would be so. It is a 4 to 1 point to put in tenders to part with the guarded by 3950 plus 200. Well, this it was again will bring this divided. But over bonfires. You don&#x27;t know music was violently forward into tenders to power. Then Divi before one buys it&#x27;ll rationalism. Do you know Senator Martin Global Want Isiro and divide by zero. So we will get Ruto 1 20 according to bend this part Then into border by zero divided by 4.501 24 into 41 by zero under root value is equal to 770. Hey, I do entertain this worth and into, uh, drying by who won by the road. This is a cool do valley We do physical toe 172 We&#x27;d fight miles wherever So therefore which one is greater than me to? They were sad labeled already 200 miles is running factor

Jayashree Behera · Answer

so orbits involves circular motion, which means that there has to be sent typical force doesn&#x27;t and centripetal force is basically the some off all the forces acting on the mass on directed towards the center off the circular motion for planets. This is the force of gravity. Therefore, the centripetal force it&#x27;s caused do the force of gravity, so the magnitude would have to be equal. Now over here to force off gravity. Questions can be substituted into this equation. So we know the magnitude, the expression for centripetal force so that there&#x27;s moss time centripetal accent. All that&#x27;s move in circular motion. John So orbits involves circular motion, which means that there has to be centripetal force doesn&#x27;t and centripetal force is basically the some off all the forces acting on the mass on director to hand over our and this is equal to the gravity. The gravitational force. So gravitational force has two equations advantage mass times acceleration due to gravity, and the other is so write down the value off centripetal force and another question for the force of gravity. Can Middleton as the gravitational constant times the planner that&#x27;s moving. They should message three squared over R, and this is equal to the gravity. The gravitational force. So gravitational force has two equations advantage mass times acceleration due to gravity on the other is so write down the value off centripetal force. And another question for the force of gravity. Can Mildred and as the gravitational constant Times capital M, which is, uh, the reason off the gravitational force over said, small lemon capital and all basically the two masses involving the force off off gravity on Dhere. Small M is moving around Capitol. Therefore, from the writing on the left hand side, we have small arms because that&#x27;s the one that&#x27;s moving around in a circle now in both of dimes, the planet that&#x27;s moving of executions, the orbiting Mars small and cancers on both sides. Now the Maas capital M in the right, which, as I already said, is the mouse off the large central star around which the other Mosses the planets, so move in a circle most since the moss off the orbiting body cancers began. Say that Times Capital M, which is, uh, the reason off the gravitational force over said small lemon capital and all basically the two masses involving the force off off gravity on Dhere. Small, um, is moving around Capitol. Therefore, from the writing on the left hand side, we have small because that&#x27;s the one that&#x27;s moving around in a circle now in both of executions, the orbiting Mars small and cancers on both sides. Now the Mars capital M in the right which, as I already said, is the mouse off the large central star around which the other Mosses the planets will move in a circle lessens the moss off the orbiting body. The equal to V squared over G. From this a question on from the 2nd 1 we have AJ to the equal toe these glad overs capital G. And so from the street questions we can say that mo matter what the value off small m is are with the equal to V squared over G. From this a question on from the 2nd 1 we have AJ to the equal toe these glad over Capital G and this Oz remains same on dhe. Therefore, we can say that all planets at the same radius will have the same all bitten speeds. If capital m which is the mouse off the large Central Star arguments unchanged. So the correct answer is going to be option beat. Thank you

Donald Albin · Answer

So we&#x27;re asked to figure out the speed of a satellite in ah, circular orbit around the earth. Well, I know that Ah, the square of the period is four pi Oh, are queued for pi squared r cubed over g m. But the period is, uh Well, let&#x27;s not go to that yet. Um, just take the square root of both sides. R cubed over G. Yeah. Now, the, um, period is two pi r over the speed. Or rather, the speed is, uh, speed of the satellite is two pi r over the period, which is two pi square root of our cubed over g m. The two pi cancels out, um, this and this cancel out, um, two of the ours in the denominator cancel out. And so it is the square root, uh, gm over r, which I probably could have just written down without going through this, but anyway, spirit of GM over R. Okay, let&#x27;s move on to be so this saddle late breaks into two masses and and for and it tells us that smaller piece is stationary with respect toe earth and falls directly toward Earth. Where has to figure out the speed of the larger piece. So I&#x27;m going to write, um that the kinetic energy before the explosion equals the kinetic energy after the explosion of the A smaller one plus the kinetic energy after this explosion of the larger one. So the kinetic energy at the beginning is 1/2 times i m although the mess of the beginning is five m and then the initial V initial squared is the square root of GM over R. So when F m. V squared is just gonna be g m over our a que kinetic energy of the smaller one says that it becomes stationary. So I&#x27;m thinking that V just ends up being zero. And so this 1/2 MV squared wouldn&#x27;t be a zero is zero um, 1/2. Now it is 4 a.m. times again g m over our we admit, Let&#x27;s not right GM over r V squared. Okay, so the one halves cancel out the EMS cancel out so the velocity will be the square root of five 5/4 g m over our Okay, so now let&#x27;s go to part C. This did increase its speed, and its gonna move into a new orbit. So, um, so we can set the square root of G M over B, which will be the distance away when it reaches the other end of the Ellipse equals the square root of four fists GM over R. So I cancel out the G in the m, invert the whole thing. Well, take the square of both sides and invert the whole thing. B equals 5/4 you are, which, by the way, is 1.25 are so it will be 25% farther away than it was before the

Ravi Lall · Answer

we need to find out the rate of change off this cave velocity from the how it changes with distance from center of the now the escape velocity formula is actually given by the escape is square root off too G mass off earth divided by our Now, this can actually be written as are to the part off, excavated and as our to the par of minus half out big. This are in the new major to GM. Hey, now you find out the rate off change or the D V escape velocity with respect to the radius, Howard is changing. So we actually finding the generative of this velocity with respect to our so we&#x27;ll find the derivative of this, which will be minus half are to the par off minus one by two minus one times do G m e. So that should give you minus have are to the part off minus three by two to g m e. So just simply applying the by the formula n xn minus one. But simple, dear innovative here. So if you sold that, simplify that he will get square root off G emi over too far cubed so that has the rate of change off the velocity with respect to or now they&#x27;re saying that we need to use an approximation that the delta we escape is equals. Two d v Escape, divided by D are so the innovative of velocity with respect to Arthur Times Delta are we have already guard this d by D. R v escape, which is negative. G m e by two are cute times Delta, Are we just looking in? The rally was here, so you will get 6.67 times turned upon negative 11 times the mass richest 5.98 times turned to the par off 24 divided by two times 6.38 times 10 to the part or six cubed. So if you solve that, then he and then sorry. This is also more deployed by delta hour which is 3.2 times turned to the par off five meters which was 320 kilometers. So we&#x27;re supposed to find out the escape velocity at a height of 3 20 kilometers used this approximation So if you sold that you know holding in the calculator you&#x27;ll get negative to 80 meters per second. So this actually means that the escape velocity has decreased by 20 meters per second at this height. So therefore we&#x27;ll have the velocity of escape is 1.12 dimes turning to the bottle for minus to 80. And if you saw that he will get approximately one point or nine times turned to the far off for meters per second. So that is the escape velocity, actually, at a height off CNN 20 kilometers above the surface, off the art.

Manish Kumar · Answer

then retied you. But it is Sophie Nous, the planet given recently called to to the 761 Oi, They&#x27;re free kind of hurt this into feed. So we were multiplied this one into five to oh, digital sort. Absolutely. This will become 19 point it pirate into to devour six. So this will become 19 point, I think 5 18 to 20 the power six feet. And in our expertise in do this one did you give him which is equal strewed 29.2 feet forsaken disquiet and the distance from the Self Aziz 100 am I So is the distance from the surface It&#x27;s 100. Am I peral distance are nice Will be nothing but this 100 hamp elicited Yes, in areas is nothing but I think 37 61 a my and we will multiply private to our Jiro for changing into the feed. So this will be coming, I think. Mm. 20.26. Inter tentative. Our six? Yes. Absolutely. If it and the no it started to fly a formula Didn&#x27;t mind speed of such a light. So we know normal exploration is nothing but you squat upon our guys with the distance from the center in the now. And this is also equals two g upon harder squad into hard as Squire. So basically this one are and one argued, cancel to be a Squire. Become nothing but g are a square upon our days. Yeah, so this will become no put on the values here and in the next step, rewriting B is directly is equal to root over the vision 29.2 into outer square. That it&#x27;s quiet is nothing but 19 point five Good. Fire it. Okay, this is the given and interjected about six Squire upon our desired as you have been looted is equals to 20 point period 20 points to the earth six into 10 to the power six. After this rhetoric calculates and this Velo city here this comes out toe 20.766 interjected the voluntary feed first again this Isabella city

Problem

For each compound, would you expect greater solub…

Problem 28 Medium Difficulty

If the speed of a satellite orbiting the Earth at a distance $r$ from the
center of the Earth is $v,$ what is the speed of a second satellite orbiting
the Earth at a distance 2$r$ from the center of the Earth?
(A) 2 $\mathrm{v}$
(B) $\sqrt{2} v$
(C) $\frac{1}{\sqrt{2}} v$
(D) $\frac{1}{2} v$

Answer

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